Since it's Original Series and therefore the most well-known, iconic characters who are destined to be recast forever now it seems, yadda-yadda... CBS could try getting a reanimation project underway. It'd sell to a network someplace, simply because it's the further adventures of Kirk, Spock and McCoy. No money to lay out on script writers, voicing talent or musical direction. Care would be needed to match new animation with the already set soundtracks.
What's the point of that? From a commercial standpoint, there's no great demand to see any sort of TAS-R production, and slapping some new animation over the Filmation voice and music score work boils down to disrespect coupled with a gimmick production.
If anyone really had a desire for a Trek cartoon, base it on J.J. Trek, and gauge the public interest. Good luck to them on that.