To predict what Star Trek: 2017 will be like, one only has to see the history of Doctor Who.
The original Doctor Who TV show was on for 26 years. By the time it got cancelled, the show had gotten old and stale, the writing sucked, people were losing interest and the BBC outright hated it. Even with Andrew Cartmel's ideas to make the Doctor more mysterious by implying he was a lot older and something else entirely than what we knew, and Sylvester McCoy's excellent take on this idea, it ultimately didn't save the show.
Fast forward to 1996. Someone has the idea to "restart" Who by making a TV movie as a backdoor pilot for a new series. And here's where they fucked up. They essentially made a fanwank film for fans only, with things only a fan would understand. They brought in the Daleks without explaining who they were. They brought in the Master without explaining who he was. They brought in the Tardis without explaining why it was bigger on the inside than the outside. They had the Doctor regenerate from an old man into a young guy without explaining just what the hell was going on. McCoy even said that the worst thing they did was have him in it. And guess what happened? No new Who from 1996 to 2005.
(Disclaimer: I loved the 1996 movie, but that's because I'm a Who fan and knew what was going on.)
Fast forward again to 2005. Russell Davies resurrects Who, but while it was always meant to take place in the original series canon, they went out of their way to make any references to the original minimal at best, and nonexistent at worst. It was based on Rose's point of view, someone who is just learning all this for the first time, so we the casual audience who never saw Doctor Who before could follow along with Rose and learn what she learns. Of course, many years later the references to the old show started peaking out more and more, but by them the show had a dedicated fanbase that could follow along and (gasp) even watch the old show to understand the references even more. It was essentially a complete reboot while at the same time still faithful to the original in just enough ways that both new viewers and old could appreciate it.
My point? A successful show must both bring in new viewers without alienating them by showing stuff from 20 years ago that they wouldn't understand, but also keep from alienating their core fanbase by radically changing what made them fans to begin with. Picking back up with the Prime timeline after all this time isn't really the answer, because unlike Who, you can't just be vague about what happened before, and new viewers most likely won't care about the Dominion War, etc. It's just unnecessary. IMHO, a full, complete reboot is the answer. Something entirely new, but still with the ideals of the original series at heart.