The flowchart in my signature will give you the big picture, all of the related post-finale books of all the different series, but without plot details.
If you'd like to catch up more specifically, probably you want to read:
- Star Trek: Destiny - a big crossover trilogy about the Borg, good starting point.
- Then, for VOY's crew: the four most recent Voyager relaunch novels, starting with Full Circle (see my signature)
- Then, for DS9's crew: the following novels from the Typhon Pact series - Rough Beasts of Empire, Zero Sum Game, Plagues of Night, Raise the Dawn
- Then for the most recent on TNG's crew: the Cold Equations trilogy.
There will be some gaps in there, but that's probably bare minimum to catch you up. (And all those books are goddamn kickass too, lemme tell ya.)
Unless you just want a whole bunch of spoilers, in which case say so and I'll give you a summary behind a spoiler warning.