Simply tag them with the movie(s) they are referring to.
I see no reason that questions about Star Trek (2009) shouldn't just be tagged with the star-trek-2009 tag, and questions about Star Trek Into Darkness shouldn't just be tagged with star-trek-into-darkness. Questions about both would simply use both tags, and questions about the upcoming sequel to Star Trek Into Darkness would use a film specific tag for that.
The reason for this is that unlike the various "cinematic universe" tags we have (such as the marvel-cinematic-universe tag, the new Star Trek films are not a "cinematic universe" as such thanks to the fact that they are just a series of films, with no spin off or related material to ask about.
Should a spin-off film or TV series be announced then this will need rethinking, but for now we should treat them the same way as we would treat any other series of films.
EDIT: It looks like the new Star Trek films do in fact have related materials. As such, I would suggest a new tag to be used when referring to this new franchise, something like star-trek-reboot. Please use the other answer to upvote this solution.