I just realized something while I was out on a walk today, two of the three people with past Trek writing experience wrote/write Voyager in one form or another. I'm not saying I expect this to be a sequel to or remake of Voy, but it is still interesting.
The creators of the show have such a tightrope to walk, between 'fan service', (by which I mean finding a way to incorporate the old show, whether that is making it part of the same continuity, or tipping their hat to what came before through references, or what have you) and making a good, standalone show, that is quality in and of itself, that new fans can come to with no knowledge and enjoy, and is sci-fi that brings new ideas to the table and follows in the tradition of Trek using allegory to wrestle with contemporary, human issues (while still standing the test of time for future generations!). Phew!
But I think the balance should always be, and I'm sure the balance will always be, towards the latter. Never let Trek's history be the millstone around your neck, as a creator.
I think watching Hannibal can be very instructive for how Fuller might approach this. He basically used the source material (the Harris novels) as building blocks for his own show, moving pieces around, hitting certain 'notes' that the novels hit. Still telling the same 'primary' story, but doing it in a way that was novel, and deep, and entirely his own, but still being respectful to the source and still functioned, on some level, as a prequel to The Silence of the Lambs.
I think his Trek might do the same, and since there are so many fans among the creators, this style will lend itself to that. Same universe, same love for sci-fi allegory, same humanism, but putting their imprint on it through new characters and stories. I think it could really work, but I hope they don't make themselves beholden to the fans. I'd love to see more Voyager, but it would alienate new viewers. Let the new show stand on it's own.