I always wanted to do a TV show that was more slice of life about what it is to actually live and work in the federation, from the point of view of a starship that wasn't the latest and greatest, where no one has gone before type. Something like an akira, miranda, etc class.
It's an old workhorse that exists to fly the flag, and works more with federation races (and non federation races that live near and around federation space), and would explore stuff like inter-species diplomacy, economics, defense, etc. Set it a decade or more after the end of the dominion war and the destruction of Romulus, prime universe.
How to tie such thought to the movies? Add a lot more politics and character action, on top of the normal action. Kirk doing more diplomacy and snark, and less hooty bang bang. Focus woudl return to the Klingons, who are on the verge of war. If Into Darkness was wraith of Khan, here is where we lay the foundations for kittamer and such.
The twist? The romulins know, thanks to Nero somehow, that their star is doomed. Que them expanding to create new colonies and such. Which brings them into conflict with the klingon empire and federation. And again thanks to nero, they (and the federation) has quite a bit more advanced tech then they should have.