Following the sacrificial death of Spock on the Genesis Planet, the crew of the Enterprise is downtrodden. They limp their way back to Starfleet Headquarters on Earth, while Starfleet hastily quarantines the Genesis Planet, making it open only to their research vessel. Onboard that ship are Saavik and Kirk's newly-discovered son, David--one of the co-creators of the Genesis device.
Back on Earth, Kirk is approached by Spock's father, Sarek, who seems deeply concerned that Kirk has somehow failed his son. He tells a dumbfounded Kirk that Spock may still be alive, if he had time to deposit his soul, his katra, into the mind of someone before death. Sarek searches Kirk's mind for signs of Spock and finds nothing. A review of the Enterprise's video logs reveals that McCoy was the last person Spock touched before death.
Back on Genesis, Saavik and David have discovered signs of Vulcan life near the casket that delivered the Spock's remains to its final resting place. They insist on beaming down to check it out. Once there, they discover that a young Vulcan child is indeed alive on the planet.
A Klingon vessel has meanwhile become aware of the existence of the Genesis Device. Concerned that the Federation has created it for military purposes, they are now in orbit of Genesis to examine the "Genesis Effect" in action. Not wishing for the presence to be relayed back to Federation authorities, they quickly destroy the Grissom, leaving David and Savvik alone with the resurrected Spock on the planet.
Kirk and crew, meanwhile, are starting to put the pieces of Sarek's mysterious puzzle together. McCoy's recently-odd behavior seems to confirm that Spock's "essence" is somehow still alive within the Doctor. Their only hope for both their living friend and their dead one, is to bring body and soul back to Vulcan, where a rite of reunification can be performed. The only problem is that Starfleet's quarantine on the planet is absolute. Admiral Kirk's superiors will in no way allow him to return to Genesis.
They thus must find a way to steal the Enterprise and probably end up losing their careers in the bargain.
After effecting an escape of the now-institutionalized McCoy, the Enterprise does a miraculous escape of its own, thanks to Scotty's sabotage of vessels likely to be sent in pursuit.
Back on Genesis, it becomes apparent to Savvik that something is "wrong" with the Genesis Effect. David admits that he used an unstable, and illegal, element in the production of the Device. The result of taking that shortcut is that the planet, and everything caught up in the Effect's matrix, are now rapidly and chaotically aging. Genesis, in other words, is dying.
Unaware of the problems with Genesis, a Klingon away team now lands on the planet, in search of the odd life form patterns below. As the Klingons are looking for David and Savvik, Spock shows signs of the rapid decay around him by growing at a dangerously accelerated rate. By the time the Klingons find and capture the Federation away team, Spock is a young man.
Now arrived in orbit around Genesis, the Enterprise is more than a little surprised to find Klingons in orbit. They're also completely understaffed for a military encounter. The Klingons demand Enterprise's surrender, showing their seriousness by killing one of the two captured adults. Unbeknownst to the Klingons, they've chosen precisely the wrong hostage to kill. Kirk is made to watch as they execute his son in front of him.
Kirk knows the odds are impossibly stacked against his six-person crew. In grief, he comes up with a solution that will save them all.
He surrenders.Thinking that the Enterprise is fully manned, the Klingon commander sends over virtually his whole crew. They don't know however, that the ship has been rigged to self-destruct.
The Enterprise crew watch from the surface of Genesis as their vessel explodes, taking with it almost all the Klingons.
Planetside, the enraged Klingon commander gets into a one-on-one battle with Kirk, and loses, just as the planet tears itself apart.
Kirk fools the remaining Klingons on board the orbiting Klingon ship to beam the entire Federation party onto the ship. Now with the odds in their favor, they easily comandeer the vessel, setting an immediate course to Vulcan.
Once there, the re-unification rite is performed the Vulcan High Priestess. After much concern, the largely untested ritual eventually bears fruit. A confused adult Spock eventually recognizes his old shipmates, and it appears as though Spock has been successfully reborn.