Given the statements said by the crew, and reading here. I'd say if the Enterprise was still operating (and I like the idea of huge damage to explain another refit) Kirk would probably be the only constant of the. Probably Chekov too, as his stand-in CO.
Scotty bought a boat so clearly has a lot of time.
Uhuru seems to be teaching.
McCoy is... well McCoy, and somehow doesn't know about Sulu.
and Spock is off starting his diplomatic career and he and Kirk clearly haven't seen each other in a while.
Everyone but Spock and McCoy I can see doing the odd mission.