Once the Abrams trilogy is completed, there will probably eventually be a new TV show. But because the movie actors will almost certainly not sign up for a series with the same cast, it's likely the series won't follow Kirk and Co.
The temptation would be to continue in the new universe with a different crew, but I feel as though that's more or less played out. What I'd like to see is an anthology series, akin to The Twilight Zone or The Outer Limits, with 2-or-3-part episode arcs following different characters and telling different stories each time.
The attractive parts about this are the freedom it allows. We can follow Starfleet characters in one story, non-Starfleet characters who are still part of the Federation, Klingons, Romulans, Cardassians, Ferengi, Andorans, Borg, Dominion, completely new races, whoever. We can move from era to era - though realistically any new series will, like the new movies, seek a broader audience than the hardcore fanbase that cares deeply about such matters.
We can tell different kinds of stories - adventure, comedy, horror, more classical SF-inclined, possibly even a romance story; anything goes. Obviously the Prime TV shows did this, but there was a certain amount of shoe-horning involved, where characters who we might have seen last week in a tense stand-off are suddenly in a comedic situation - this would allow us to avoid that dissonance.
The problematic areas are twofold as I see it. Firstly there's the budget. The Prime TV shows were expensive enough, and they had the benefit of constantly re-using sets, costumes and effects shots. So it might be that an anthology show, without those benefits, would be prohibitively expensive.
More broadly, as of late the trend in television is towards greater serialisation, towards season-long, character-driven arcs rather than the episodic fare of old. This might be seen as a step backwards.
But if it could work, I think it could be an amazing new direction for Star Trek on TV. It's a bold step and one that would likely attract a lot of disdain from the old guard even before shooting began, but I also think that done right, it could really be both excellent Trek and very successful.
Does something along those lines seem appealing to anyone else?