I haven't come across anyone mention the idea of playing with the chronology of events the way the second and third Jason Bourne movies did; ISTR it came up often when in the early stages of conceptualizing this latest ST movie. Most people assumed that meant cramming large chunks of this movie's narrative in between scenes from Star Trek (2009).
The thing is, everyone was eyeballing that gap between the Enterprise escaping the red matter black hole and Kirk's promotion to captain; yet with this new movie there's a massive gap of time between Kirk's recovery scene and the re-christening/memorial scene that's more obviously suggesting the Bourne influence.
The next movie might very well play out the aftermath of Wrath of Khan in the sense that in the "third" movie shows the Enterprise in a state of disrepair, yet pressed into service out of dire need.
Also, anything could have happened with the Klingons. As some people pointed out, a very serious potential diplomatic incident occurred with the Enterprise's actions in Klingon space, which demands immediate follow up.
And Khan is shown to be re-frozen as a cutaway that is paired with Kirk's speech at the re-christening. The details of what happens to Khan between getting knocked out by Spock and then getting put back into cryosleep are something of a question mark (that admittedly doesn't have to be answered right away, but it looks like some space has been left there to fill in some blanks.