Admiral Kirk and his bridge crew risk their careers stealing the decommissioned Enterprise to return to the restricted Genesis planet to recover Spock's body.
This movie contains 16 potentially triggering events.
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3 characters are taken hostage by Klingons. McCoy is locked in, and guarded, in the equivalent of a holding cell room, though he does not appear distressed by this. He is just shown resting when Kirk comes in.
A klingon gets disintegrated after being shot with a disruptor pistol, with a visual effect similar to bring consumed by flames.
Another character falls into a pit of lava but their death isn't depicted in any detail.
A character fights with a Klingon who was about to kill another character and is killed instead. Kirk sacrifices his career and his ship to save Spock.
About 30 minutes in, there's a prolonged moment of squishy noises created by mutated microbes. A few minutes after that, an alien in the bar is shown and heard slurping liquid loudly from a straw.
Comments are made about a man suffering from a mental breakdown planning to be shipped off to a "Federation funny farm" because he's "fruitier than a nutcake".
SPOILER
Spock undergoes pon farr while he rapidly ages and saavik has to help him through it. Nothing explicit is on screen, and the extent of it shown is a vulcan kiss (with their hands) between the two thats meant to calm spock down
(spoilers) They find Spock and bring him back. His mind, body, and memories are undamaged. Kirk loses his son and the Enterprise, but everyone is happy and hopeful at the end.