Kirk (William Shatner)’s Timeline and Summary

Kirk confers with the crew and decides to return to Earth to accept punishment for his actions in the previous film.
On the way home, Kirk learns about the probe.
Kirk and company time travel back to 1986.
There, Kirk and Spock find two humpback whales at a local whale institute.
Kirk flirts with the whales' handler, Gillian Taylor, and tries to convince her to let him take the whales.
Gillian reveals that the whales have already been released into the wild.
Kirk, McCoy, and Gillian rescue Chekov from a hospital. They pick up the whales and travel back through time. They save the world.
Kirk receives his "punishment"—he is demoted from admiral to captain and given control of Enterprise. This is what he's wanted for a long time.