In the previous movie, Star Trek II: The Wrath of Khan, Spock had sacrificed himself to save the ship and its crew. The planet where he had been laid to rest, the Genesis planet, was home to a device that had the power to completely transform a planet into a habitable world.
When Kirk discovers that Spock's memories and consciousness have somehow managed to survive, he becomes desperate to save his friend. However, the Genesis planet is now off-limits, as it is being closely monitored by the Federation to prevent any unauthorized use of the device. Kirk knows that he cannot simply ask permission to venture into the planet, as the Federation would refuse to take such a risky mission.
Kirk decides to take matters into his own hands and recruits his closest friends - McCoy, Scotty, Uhura, Sulu, and Chekov - to help him steal the Enterprise. The ship has been decommissioned and is due to be destroyed, but Kirk believes that it is still the best chance they have to get to Genesis.
Their plan is almost derailed by a group of Klingons who are also interested in the Genesis project, but the Enterprise crew manage to outwit them and make it to Genesis. There, they find that Spock's body has somehow been regenerated by the planet, but he is still in a child-like state.
As they attempt to leave the planet, they are attacked again by the Klingons, who are determined to take the Genesis device for their own purposes. In a tense battle, the Enterprise is severely damaged and Kirk is forced to sacrifice the ship to save his crew.
With Spock, the crew heads to Earth on a commandeered Klingon ship, where Spock undergoes a dangerous and experimental procedure to restore his memories and consciousness. In the final scenes, the reborn Spock reunites with his friends, creating a sense of hope and renewal for the future of Star Trek.