I was saying this elsewhere; It would have to be while Pike is away on a mission of sorts, and Kirk only deals with Spock or Number One.
Agree completely..... already annoyed that they've dumped Boyce, ignored Jose Tyler, and metamorphed Yeoman Colt..... Uhura, Chapel, M'Benga, Spock, now Kirk? Sulu amd Scotty easily could have been there too, if they keep going in this direction....
I kind of assumed that he did, and that the other ship is where he requested Mitchell as part of his first command.
I really hope they shy away from the Kirk cliches and pop culture version of him, and remember he was a serious officer and a stack of books with legs.