Lightspeed Leapfrog

The brave explorers or colonists set out in their spaceship to spread humankind to the stars. You can't travel faster than light, so they're going to spend most of the trip as Human Popsicles, or it's a generation ship and it'll be their descendants who step out at the other end of the trip. Either way, they're saying goodbye forever to everyone and everything they know. Decades and centuries pass, and eventually they arrive at their destination--

--and there's people there waiting for them. Turns out, Faster-Than-Light Travel is possible, and it got sorted out while they were in transit. Now the same trip that took them centuries can be done and be back in time for Christmas. And that planet you were all set to colonise? Done already, and actually we're not sure there's any room for you...

Expect the brave pioneers to be upset about this.

Can be related to Humans Advance Swiftly.

Examples of Lightspeed Leapfrog include:

Comics

This was the origin of Vance Astro in Guardians of the Galaxy. He was cryogenically frozen and sent on the first manned space mission to another star. When he arrived, he discovered that Earth had invented faster-than-light travel and had colonised the world he was heading for. He was hailed as a hero but found he had arrived in a world where he no longer had a place.

Literature

In "Founding Fathers" by Stephen Dedman, the first FTL ship shows up after the colony's been established for a few years, but it's still a shock and an upset to the colonists, who had actually embraced leaving everything-and-everyone behind because it meant they'd be left alone to do things the way they think things ought to be done.
"On the Road to Tarsus" by Sean Williams is a variation involving long-range Teleportation: the first generation where the signal travelled at light speed and the later FTL Radio refinement that meant people could cross light years in a matter of days. Tarsus is Earth's first extrasolar colony, thirty light years from Earth, founded using the newer system while the original set of colonists were still en route at light speed; as the story closes, the planet is preparing itself for the imminent arrival of the original colonists-to-be.
In Time for the Stars by Robert A. Heinlein, the protagonist is on a NAFAL ship that spends most of the book exploring the nearby stars; at the end of the book when everything is falling apart, they get rescued by an FTL ship that's been developed on Earth in the interim.
In Mostly Harmless, we're told that one of the things making Galactic history so confusing is the armies that were sent out in sleepships to fight wars with distant civilisations, only to awaken, discover that diplomats travelling FTL arrived before them and hammered out a peace treaty, and damn well fighting their wars anyway.
Happened to several groups of colonists in the backstory of the Honor Harrington series of books. On at least one occasion, lead to a planet being home to two distinctly different cultures with separate governments.
- The Crazy Prepared nature of the original Manticoran colony meant that this worked in their favor. When they left FTL travel was possible but extremely dangerous prompting them to travel sub-light. However before leaving they invested their remaining money with instructions that when safe FTL travel was invented the money should be used to contact them and if necessary prevent other people from establishing a colony on their planet before they arrived. Consequently when they did arrive they found a small squadron of warships guarding their home and all of the equipment and teachers necessary to bring them up to speed on 800 years worth of scientific advancement.
Charles Sheffield's Summertide starts with ships carrying Human Popsicles. They are programmed to wake the people if they reach the destination, if a problem arises the computer cannot solve—or if they receive a transmission that FTL has been invented.
In the final book of Harry Turtledove's Worldwar series, Homeward Bound, a human-built sleeper ship is sent as an embassy to the homeworld of the reptilian Race. The trip takes about 30 years to accomplish. The ambassadors are only at the Race's homeworld for a month when the human-built FTL-ship shows up.
Played with in Larry Niven's short story "Flatlander". The Outsiders (a race of Starfish Aliens who are the ultimate Higher-Tech Species in Known Space) sell the location, trajectory, and velocity of a lost colony ship to the humans, who later use their FTL technology to rescue the crew and colonists on that ship, all of whom were in stasis.
A. E. van Vogt's "Far Centaurus" is about a group of people who are trying to be the first to reach Alpha Centauri, but along the way somebody up and goes and discovers FTL travel.
Part of the backstory in Strata.
Pandoras Star by Peter F. Hamilton starts out with a variation. A NASA vessel makes humanity's first-ever manned voyage to another planet (Mars), only to discover that a pair of garage inventors have discovered the means to generate stable wormholes and beat them there.
Mentioned in the Strugatsky Brothers' Noon Universe. No FTL travel actually exists there, but one character mentioned how terrible it would feel to be an astronaut on a relativistic ship sent to explore a distant star only to find a colony there established by an FTL-calable ship developed after you left. Additionally, by using high acceleration on a relativistic ship, a crew manages to reverse the effects of Time Dilation (i.e. six months passes on Earth, while years pass for the crew).

Live-Action TV

Babylon 5, "The Long Dark": In the 22nd century, the exploration ship Copernicus set out with a frozen crew and a navigation computer set to track down radio signals suggestive of intelligent life. A hundred years later, it arrives at the source of one such set of signals—Babylon 5. Turns out, the Centauri found Earth and gave humans jump gate technology just a few years after the Copernicus set out.
The season 1 finale of Star Trek: The Next Generation, "The Neutral Zone", is in part about a recovered ship sent from Earth in the pre-warp era, with cryogenically frozen passengers.
In the Andromeda episode "The Lone And Level Sands", the crew encounters a 1,700 year old exploration vessel. Its mission was scheduled to last 3,000 years.
- The crew (most of them, anyway) of the Bellerophon is fully committed to continue their mission, even though they know that there's no need for relativistic travel given the existence of slipspace drives. Of course, the captain of the ship has known about this for far longer than most of his crew and kept the fact hidden in order to continue the mission.
A mild version of this in Stargate Universe, where descendants of an alternate version of the crew of the Destiny have a 2000-year colony on planet Novus. However, as the planet is destabilizing, they have built sublight generational ships to take them to a world their advance scout teams found using stargates. The Destiny crew (not the alternate one) find one such scout group and decide to give them a lift to their destination, knowing that the generational ships will get there in about 200 years.

Music

"Space is Dark" by Bill Roper is the story of a crew who awake from centuries in suspended animation, ready to seek out habitable planets, to find that humanity has spread across the galaxy using a hyperdrive invented shortly after they left Earth. They don't take it well.
On the other hand, Compound Interest, also by Roper with Duane Elms, tells of a crew who, rather like the Manticorans, invested their hazard pay at very lucrative rates with the provision that after 500 years the large amount they'd built up was to be used either to invest in offworld development, or to develop hyperdrive, if it didn't already exist, as their sole property. When they awake from frozen sleep after a thousand years, they're the richest people in the galaxy. Incidentally, the first three words of Compound Interest are, "Space is dark," so Mr. Roper may have deliberately set out to give two possibilities of the same basic idea.

Ten years from when we set the quest,
They found the hyperdrive,
And Man spread to a million worlds,
And we own all but five.
For we control all commerce;
Any trade must be our trust,
And every ship that moves
Must lease the hyperdrive from us!

Video Games

The Forsaken in Vega Strike are the whole faction formed from the settlers who arrived to their destination only to find already developed places where no one needed them. Forsaken are understandably bitter about all this and ended up as one big pirate haven.
The manual for Elite says you can encounter ancient generation ships still flying to their destinations in your Casual Interstellar Travels. You can't, but if they were in the game, that would be this trope.
- However one of the user-made addons for Fan Remake Oolite adds these into the universe.