It seems like none of the senior staff are still assigned to Enterprise
at the start of Star Trek VI: The Undiscovered Country
. Given that Spock is the Federation Envoy to the Klingon Empire, perhaps he'd arranged to have Kirk, Scotty, Uhura and Chekov returned to the ship especially for the mission. They could have been off elsewhere doing other things. Uhura especially points out that she's teaching at Starfleet Academy. Perhaps Chekov was away serving on another starship.
Personally, I'm surprised Sulu didn't request him for the position of Executive Officer aboard Excelsior