Every new version of the warp drive in Star Trek
Star Trek's warp travel was the common standard for three centuries, but it's been given a major upgrade in recent times.
Star Trek popularized the term "warp speed," but the franchise has created several alternatives to travel via warp drive technology. By the time of Star Trek: The Next Generation, warp drives had been around for about three centuries, and had come a long way since Zefram Cochrane's first warp flight. The warp drive allows Star Trek's starships to locally warp the space-time continuum by creating a warp bubble, allowing the ship to travel at a certain degree of warp speed, thus traveling faster than the speed of light. It was the most widely used form of interstellar travel in the 24th century, but some alternatives have recently been introduced out of necessity.
Star Trek Discovery season 4's tragic villain, Ruon Tarka, is looking for an alternative to warp travel after suffering the devastating effects of a conflagration. As the dilithium needed for warp drive technology has been largely depleted and is at risk of instability, the Federation is researching and advancing Discovery's spore drive technology. However, this is just one of many alternatives to the warp travel recently introduced in the Star Trek canon.
The Spore Drive
The spore engine was introduced in Star Trek: Discovery Season 1 and co-opted by Starfleet Paul Stamets and Straal to gain an advantage in their war against the Klingons. Stamets and Straal's research is based on the idea that at the quantum level, the universe is no different from living organisms. The implication of this discovery is theory that a starship, with the help of a suitable navigator, can traverse a network of spore spaces known as the mycelium network.
This was a groundbreaking discovery that led Discovery to abandon warp travel in favor of this more organic approach. However, it's not without its drawbacks. Although the spore drive allows for near-instantaneous traversal of the web, it may cause physical damage to the navigator. Starfleet began investigating a non-human interface, but the research was abandoned and evidence of the drive was suppressed when the Discovery was lost in the Red Angel event. The Federation of the 32nd century has now picked up where the 23rd century left off.
The concept of interstellar travel was introduced in Star Trek III: The Search for Spock, when Starfleet attempted to install a interstellar travel drive on the USS Excelsior. However, it remained a theoretical concept until Picard's Enterprise met the Borg. Borg Travel across the galaxy at speeds beyond traditional warp travel using warp-span technology. Later, Admiral Janeway will take advantage of this when she goes back in time to get Voyager home faster.
To date, no one has been able to install a transwarp drive, presumably because better alternatives have been discovered. Another downside of the trans-warp drive is the severe mutation Tom Parris underwent when trying to break the trans-warp barrier in his attempt to bring Voyager back to the Alpha Quadrant. A safer alternative was also discovered during Voyager's time in the delta quadrant.
Quantum Slipstream Drive
Admiral Janeway's new starship attached to Voyager and its time in the Delta Quadrant. The USS Dauntless has a quantum slipstream drive, meaning the starship is capable of traveling at speeds far beyond the capabilities of standard warps. This was necessary for Janeway's mission to return to the Delta Quadrant to recover the Protostar and discover the whereabouts of her former Chakotay One. In the season 4 finale "Hopes and Fears," the Voyager crew first discovered the quantum slipstream drive when it was used as bait in a revenge plot against Janeway and the crew.
In the Star Trek: Voyager season 5 episode "Eternity", the crew attempted to build their own quantum slipstream drive, but due to a miscalculation, Voyager crashed into a planet, killing everyone. Chakotay and Kim need to go back in time and fix the miscalculation. Their mission leads them to meet TNG's Geordi La Forge, who tries to stop their dangerous time plot. To correct their mistake, Voyager abandoned the slipstream technology experiment. Sometime after Voyager returned home, Bellana Torres led the construction of the aircraft carrier USS Intrepid equipped with quantum slipstream drives.
The Protostar Drive
Star Trek: Prodigy introduces the USS Protostar, an experimental starship with a new power source, a real star. Protostars, the earliest stages of stellar evolution, subtly mirror the young members of Prodigy. While the protostar drive still required a dilithium matrix to operate, it traveled far faster than any other ship in the fleet. It's implied that the Protostar was sent to the Delta Quadrant to fix some mistakes made by the Voyager crew there. The captain of the ship is Chakotay, who is now missing along with the rest of the crew.
Janeway was present at the launching of Chakotay's new starfleet and was personally tasked with tracking down the missing ships. The USS Protostar is the most advanced ship in the fleet, and Starfleet fears it will fall into the wrong hands, unaware that it has already. So far, the Protostar's crew has been able to outrun the Dauntless and protect the Federation from the weapons within the ship. However, Prodigy reveals that quantum slipstream drives and protostar drives can achieve similar speeds, so it only takes one misstep for the highly advanced USS Protostar to be recaptured, spelling disaster for the Star Trek Federation.