Student and Master Team

Always two there are, no more, no less - a master and an apprentice

—Yoda, Star Wars: The Phantom Menace, on the Sith.

A variant of Odd Couple featuring an older veteran character, and a younger novice. Often the former is a Retired Badass who is somehow rendered powerless (or just helpless against current threats) and has to rely on a newbie, who happened to be around and accidentally shows a lot of promise, so he tutors him.

Perfect setup for Red Oni, Blue Oni - the Hot-Blooded younger character is kept in check by their Older and Wiser Mentor.

If they're cops, this is Old Cop, Young Cop. If they're father and son, see Badass Family. If they happen to be a gay couple, see Lover and Beloved, and if heterosexual, see Mentor Ship. With magic users, see Merlin and Nimue.

See also Sempai-Kohai. Master Apprentice Chain is when this trope is recursed over several generations.

Examples of Student and Master Team include:

Anime and Manga

Mireille and Kirika from Noir.
Bleach starts out like this, with Rukia losing her shinigami powers to Ichigo.
The first season of Magical Girl Lyrical Nanoha, with Yuuno getting injured and going ferret mode to recuperate, requiring him to rely on the then ordinary elementary school student Nanoha. Except that Nanoha completely overshadows him in a few eps.
- The StarS and Lightning Teams in StrikerS consisted of two experienced instructors and two students.
Robin Mask and his disciple Warsman form the Choujin Master/Student Combo in Kinnikuman's Dream Tag Team Touranment arc. Though the two are on more equal footing than most examples.
Whenever Kenichi of Kenichi: The Mightiest Disciple gets thrown into one of these with any of his masters (and it happens a lot), it's not because he's needed, its because the masters want to train him by having him fight their opponents' disciple.

J and K from Men in Black.
Both the Jedi and the Sith in Star Wars tend to work in teams like this.
- Notably Qui-Gon/Obi-Wan, Obi-Wan/Anakin, Obi-Wan/Luke, Sidious/Maul and Sidious/Vader.

Numair and Daine in The Immortals quartet. Until she gets Hot for Teacher, anyway...
Older Than Feudalism: Elijah and Elisha in The Bible.
Vimes and his younger self in the Discworld novel Night Watch.
- Lu-Tze and Lobsang in Thief of Time.
- Granny Weatherwax and Tiffany in A Hat Full of Sky. Nanny Ogg and Tiffany in Wintersmith. Interestingly, not Tiffany's official witchcraft teachers, who are helpful, but don't exactly fit the trope. Other times the witches fall into The Hecate Sisters ensemble.
That's what happens with Aahz (who is Brought Down to Normal mage) and Skeeve (who learns magic from him) in Myth Adventures by Robert Asprin.

The Doctor and his companions, although less so with the reboot's tendency for younger (-looking) Doctors. Also, there's never any suggestion of them filling his shoes, for obvious reasons.
- With a few almost exceptions - Romana leaves to serve a similar role in another universe, while the never completed plot arcs may have had Ace eventually becoming a Time Lord. Sarah Jane also gained a similar role in her own spin-off, complete with apprentices of her own.
Reid and Malloy in Adam-12
A staple of Highlander, where veteran immortals would train newborns.
The Mystery Science Theater 3000 episodes "Master Ninja" and "Master Ninja II" feature a team like this, in the form of Lee Van Cleef and Timothy Van Patten, as does "The Master," the TV show from which the movies were hastily spliced.
Power Rangers sometimes uses a team version, where the Mentor suits up and takes the field with his students as a Sixth Ranger. Mentors that have done this include Dr. Tommy Oliver, Commander Cruger, Daggeron (and Udonna and Leanbow on occasion), and RJ.

In a similar vein would be Shingetsutan Tsukihime where we have Arcueid The Ultimate Vampire Hunter who loses her powers and has to rely on Ordinary High School Student Shiki, who just happens to have the Ultimate Evil Eyes.
Kreia and YOU in Star Wars: Knights of the Old Republic 2
In Suikoden, the hero's mentor is one of the Loads and Loads of Characters you can recruit. They can even do a Combination Attack called "Master-Pupil Attack", where they beat up every enemy on screen together.
Disgaea has an entire mechanic where characters can serve as mentors to other characters they were used to create with useful advantages for both (for example masters can use the skills of any apprentices that are nearby).