Skilled but Naive

They don't call her Wildfire for her surgical precision.

Old age and treachery will beat youth and skill every time.

—Proverb

You get a young character who is, frankly, pretty awesome at what they do. They out-perform the grizzled veterans at everything they put their minds to, be that bringing down the Monster of the Week, commanding the Redshirt Army into battle or solving the murder. A few years older and they'd be a total Badass.

Just one problem: Their complete lack of real world experience.

These characters talents may serve them well in a professional context, but they still find themselves running into trouble by doing things the superior experience of their less talented predecessors would tell them to avoid. This is often exacerbated by arrogance from the rookie who finds himself outperforming people who have made kicking ass their career, and Pride, as well as occasionally a sense of responsibility to use their new abilities to the fullest, not having the patience and foresight more experienced characters have in knowing you can't help anyone if you are dead.

Many, many heroes start off this way. Due to The Hero often starting off as the least experienced member of the Five-Man Band, giving him room to grow as a character, but also tending to ultimately be the most powerful member of his team, main characters in general have a nasty habit of going beyond their experience levels and relying on raw talent and bravado, which frequently gets the rest of the group into trouble as well. In particularly tragic circumstances, such impetuousity can get a character or his allies killed, with all the emotional torque and lessons about the fragility of youth and the dangers of overestimating your talents such an event provides. Its a frequent source of the Mentor Occupational Hazard.

Kid Heroes, such as Young Guns, Kid Samurai and Cute Bruisers can find themselves falling into this. Add Hot-Blooded into the mix and you're asking for impetuousity combined with incompetence.

This trope is very closely related to Idiot Hero, to the point where the two tropes look identical at first glance. There's a subtle difference however. While Idiot Hero refers to a character who is genuinely intellectually challenged but whose other strengths (Heroism, personality and morality) make them heroes, characters of this trope may be very intelligent, possibly even geniuses... but they don't have enough experience, both in life and in their chosen fields, to make the best of that talent. Its a subtle difference, but an important one. Though an Idiot Hero can easily also be Skilled but Naive if their usual line of work tends to rely more on instinct and moral certainty than on abstract intelligence, and naturally the lack of intelligence will tend to exacerbate their naivete.

If and when they do evolve, they are rather malleable. A bad shock may send them into themselves, creating a Zen Survivor or Knight in Sour Armour, a character who feels cynically about issues but still can't stop the bold idealistic tendencies from showing through when the chips are down. Or constant steady success may create a full-on Badass or messiah. They can easily become a Future Badass in cases of Sacrificial Lion or an earlier Downer Ending where this character survives.

Note that to fit this trope characters have to be:

1) Just as powerful or more powerful than more experienced characters

OR

2) Noticeably remarkable in their skills for their experience level

AND

3) Naive when it comes to comprehending the world around them, subtle meanings of things, and the like. (These characters are likely to be Wide Eyed Idealists and believe in Honour Before Reason)

4) While being excellent technical fighters and academically very capable at what they do, they are vulnerable to tactical oversights that only a more experienced character could possibly pick up on.

Examples of Skilled but Naive include:

Anime and Manga

The main character of Naruto
- In Shippuden he is (though he's growing out of the naive part while still being idealistic) but at the start of the story he didn't even have the skilled part until he mastered the Kage Bunshin Jutsu.
  - Itachi Uchiha claims that his younger brother is one of these (Hence the manipulations of Orochimaru, Madara/Tobi and to some extent Itachi himself.)
Ichigo of Bleach is one of the most powerful Shinigami in existence and quickly reaches the level of the Game Breaker captains, but he lacks the years of experience the aeons old Soul Society members have under their belt. Even the Seireitei's Kid Hero has four to five decades of fighting and training experience, though of all the captains, he is also given to rash moves. This lack of experience and naivete shows in Ichigo letting himself get manipulated by the Big Bad during the Hueco Mundo arc as well as in his brute-force fighting style, and is a textbook example of the trope in action where you have an overpowered, multi-class character with no idea of how to use his power most effectively. (His strategy amounts to "Hit it until it falls down.") That said, this is also Ichigo's strength along with many heroes of this type: his actions are so reckless, and yet he is so overwhelmingly powerful, that he catches enemies completely off-guard, even when they are expecting him. Ichigo's lack of experience also makes his performance inconsistent; he can be the world's biggest badass if he's in the right mood and barely able to match the much weaker lieutenants if he's on bad form.
Azuma Kazuma of Yakitate!! Japan. He's an excellent baker, but has little experience due to growing up in a remote rural area. He didn't even know what nan bread was, "inventing" it himself without realizing it had already been invented.
Tamaki of Bamboo Blade. Absolute prodigy at swordplay, hopelessly naive in other situations.
Negi Springfield from Mahou Sensei Negima, a highly talented mage who at 10 years old has the sort of power and skill that most don't get even after decades of study and training...but he's still a ten year old and he thinks like one. As a result, a good chunk of his training involves getting the naivete beaten out of him.
In the beginning Goku from Dragon Ball lacks even the most normal skills, such as personal hygiene, maths, social skills and the like... he gets better along the story but remains naive enough to fall for the oldest and dumbest tricks in the book... he's also a powerhouse of brute strength, agility and endurance AND he's a genius in all things related to martial arts. Clearly Sacrificed Basic Skill for Awesome Training.
Luffy of One Piece: a strong and determined character who is made of rubber... who also goes "WOOOOOOOW" at every little thing along with Chopper, and who lacks common sense in many(most) occasions... like Goku above he also gets better, sorta, as the story progresses.
Shichika of Katanagatari: He's spent his entire life on a remote island cut off from civilization with only his sister and his father. He can't even tell other humans apart from each other by sight alone. While he did receive 20 years of training in Kyotoryuu, a powerful fighting style that is essentially "swordsmanship without a sword", he lacks actual battle experience. This actually cost him a quick victory in episode 2 when he was caught off guard by his opponent's sword pressure and inadvertently held back on what would have been a decisive blow. Fortunately he had a backup plan in that case (which also doubled as a Crowning Moment of Funny).
Woli from Hajime no Ippo is absolutely made of this trope. That's what you get from being a divine boxing genius who got the Indonesian title after three fights. He's a happy-go-lucky monkey boy who makes stupid moves such as talking to his opponent during the match and eating bananas before the match, yet is basically the Takamura of feather-weight in terms of natural talent and fighting instincts. The only reason he lost against Ippo was due to lack of experience. Even Coach Kamogawa admits that Ippo couldn't win against a Woli with more boxing experience.
- Itagaki Manabu is a good example as well, albeit not as extreme as Woli.
Teana Landstar of Magical Girl Lyrical Nanoha fame has the Young Gun trait. Her Character Development is chiefly about getting over herself and learning to be a team player.
Romeo X Juliet: Juliet, oh Juliet. You're a total Badass Adorable, but you should've known better than falling for the cute guy in a Cool Horse...
Dr. Tenma in Monster. He's a surgical prodigy and an excellent doctor in general, but he's completely oblivious about Dr. Heinemann's political games, and that costs him the life of a patient he could have saved. After that, he gets better and evolves into The Messiah.
This trope is addressed in Samurai Champloo: One of Jin's early opponents, Inuyaka, notes that while he's a very skilled swordsman, he hasn't had enough outside experience to fight him in an unfamiliar environment, as he's spent his entire life training in a dojo. (By contrast, his counterpart Mugen wouldn't know formal fighting if he was presented with an instruction manual.)
Haqua du Lot Herminium of The World God Only Knows was a brilliant student, whose hard work and talent were so undeniable that she broke through the glass ceiling and became the first student from a lower-class family to ever be awarded the Scythe of Testament, signifying her place at the top of her class. Once put in the field, however, she causes trouble by losing patience with her human partner's Gradual Grinder approach, due to her need to prove herself. Then, when Vintage rears its head, she proves to be woefully naive when it comes to reading people, requiring the help of her more worldly acquaintances on numerous occasions.
Pick a Gundam protagonist. Amuro, Kamille, Kira, Shinn, even the supposedly cynical Setsuna all start out pretty naive. Then they get caught up in the war and, in one way or another, all break.
Priscilla from Claymore fits this with tragic consequences. She hadn't been on the job for long before she was promoted to number two in the organization, and she was truly skilled at what she did. However, her big flaw was that she lacked experience and tended to see everything in black and white, even when fighting yoma. Both Teresa, who she was hunting, and Illena, who was really in control of the entire assassination task force (albeit it was technically Priscilla since she outranked her), called Priscilla out on her naivety, but seeing that Priscilla was also emotionally unstable do to her traumatic past - you can guess where everything eventually led to.

Literature

In Five Hundred Years After by Steven Brust, Mario is hired to assassinate the Emperor because he fits this trope. He's being set up to fail; he doesn't. In all the other books where he appears or is mentioned, it's enough later that he's become an Old Master.
Corporal Carrot Ironfoundersson in his first two appearances in Discworld. He adapts very quickly.
A Song of Ice and Fire
- Brienne is a woman in a male-dominated society and is able to fight on equal level with many of them in a stand-up fight—the first thing she does on screen is defeat Loras Tyrell, the Knight of Flowers, who is widely agreed to be one of the greatest fighters alive. Even Jaime "Kingslayer" Lannister admits she's stronger than him, though he also says she needs more experience to be truly deadly. Unfortunately, Brienne is a Wide-Eyed Idealist in a Crapsack World where Anyone Can Die. This doesn't work very well for her.
- Robb Stark is an incredibly skilled battle commander despite being only 16 and never going to war before. He won every battle and showed exceptional cunning in his strategies. But his inability to fully grasp the bitterness and potential for treachery in the likes of Walder Frey and Roose Bolton, utter naiveté about Greyjoy and Iron Island family dynamics, and his insistence of Honor Before Reason regarding Jeyne Westerling led to him losing the war and his life.
Matteo Ta'anari of Someone Elses War is clever and tenacious, but completely unprepared for military life. Which, as a newly conscripted Child Soldier, may not be in his favor. On the other hand, it's what motivates him to organize a grand escape.

Live Action TV

Spencer Reid from Criminal Minds fits this trope. His extraordinary intelligence makes him a valuable asset to the team but it is frequently mentioned that he is naive and maladjusted.
River Tam from Firefly.
Chuck of... Chuck starts off this way.
Data from Star Trek: The Next Generation is, in his words, "designed to surpass humans both mentally and physically". He can perform complex calculations in his mind in mere milliseconds. But when it comes to interacting with people...

Tabletop Games

Eclipse Phase: anyone with the Real World Naivete trait, especially artificial intelligences (which come with RWN by default).

Video Games

Liara of Mass Effect. Young, inexperienced, and will fry your brain or throw you across the room if you piss her off.
- Keep in mind that she is only "young" by asari standards. In human years, she's over 100.
- Not anymore in Mass Effect 2 as the Shadow Broker's attempt to do Shepard harm two years before have turned her into a character hellbent on getting revenge.
- Tali is also an example: While not as naive as Liara, she did go to the Shadow Broker for protection, which everyone knows is a bad idea. This almost gets her killed twice over.
Princess Tana from Fire Emblem: The Sacred Stones starts like this. She is a Plucky Girl with quite the talent to ride pegasi and use a Blade on a Stick, but she's also very sheltered by her brother and has just finished her official training. This leads her to catch a huge Distress Ball in Ephraim's route, but with some training, she can become quite the powerhouse.
Sanada Yukimura from Sengoku Basara is this trope personified. He's hotblooded and impulsive, doesn't know the first thing about strategy but is skilled enough to take down most enemies, and those he can't he takes down through sheer determination. It's also implied that he has a great deal of potential that hasn't been unlocked yet, mainly due to his lack of experience, forethought and gullible personality.
Merrill of Dragon Age II is a young Dalish elf who happens to be a brilliant mage and excellent historian. Aside from a mage Hawke, she's the single most powerful member of the party. Unfortunately, she's had next to no life experience and, as a result, she's a gullible, distracted ditz with almost no common sense. If it weren't for the fact that half of the party looks out for her, she'd probably never have survived her first year in Kirkwall.
N of Pokémon Black and White is very good at his job (Extremist?) Because he is a VERY naive person. Its even mentioned in-game

Web Comics

Yuri of Exterminatus Now is a prodigy with her dual beam swords, able to cut in half a speeding vehicle with a single slash. Unfortunately, she's not very good at listening to orders having been raised as a demon hunter to... you know, slay demons. So she's not so great at dealing with the more subtle approach the inquisitors have to adopt. (Not that they're exactly great at it.)
- Not to mention that in the incident mentioned above she got chewed out immediately afterwards for destroying the very evidence that they were trying to secure by stopping the vehicle.

Western Animation

Aang the Avatar is like this in the first half of Avatar: The Last Airbender. He's so naive and kinda ditzy that characters easily forget that he's already a master-level airbender when the show begins. The fact he's a 12 year old kid doesn't help, either.

Real Life

This can happen in educational tracks that go from high school to university to post-graduate degree without including practical applications of theory driven work.
This is sometimes the case with Military Officers. Take a newly minted Officer from West Point. He's attened Airborne School, Air Assault School, Ranger School, and had 4 years of Officer training, but when he's put in charge of a platoon of combat-proven soldiers, he will be a bit naive. The Navy, Air Force, and Marines are no exception.
- Just about every military novel, ever, will mention how an green Lt. (or equivalent) needs to be paired with an experienced NCO in order to not screw up.
There is an old saying in spanish speaking countries: Más sabe el diablo por viejo que por diablo. Roughly: "The Devil is wise not because he's the Devil but because he's old".