Metamorphosis
Captain Kirk, Mister Spock, and Doctor McCoy are returning to the Enterprise in the Galileo from peace negotiations on Epsilon Canaris III with assistant Commissioner Nancy Hedford when they encounter a mysterious force that brings them to a planetoid with a breathable atmosphere. They left the peace negotiations, which were incomplete, because Commissioner Hedford had contracted Sakuro's Disease. She isn't showing any symptoms yet but she needs immediate medical treatment.
They find Zefram Cochrane, a human living on the planetoid. He was marooned there more than a century before. The Companion, the mysterious force that brought the Galileo there, restored Cochrane, who was in his 80s when he arrived there, to his youth. It kept him from aging. It won't let any of them go because Cochrane needs other humans to keep him company and because it can't leave the planetoid.