Just a question: What is it that makes a Voyager novel a Voyager novel? Or a TNG novel TNG? Or a DS9 novel DS9? It has to be more than the starship or the starbase, doesn't it? It has to be the characters.
Honest, non-snarky answer here? Characters, as you say, are key. A continuity of characters is important (except maybe in DS9, which is tied
much more to the setting)
However, change in cast is okay and even good. The key word is
continuity, not
stasis.
So say, some characters leave, new characters come on board and are established. New characters become established, remaining old characters leave (perhaps not all at once), and newer characters come on board. New characters have become old characters, newer characters are new characters. Continuity is maintained, even though the original cast is negligibly present. New "old" characters leave after newer characters become established, even newer characters are introduced.
Let's take, for example, DS9.
End of series, crew is split up. Sisko's with the Prophets, O'Brien's on Earth, Worf's on Qo'Nos, Odo's with the Great Link, Garak's on Cardassia. Other background characters have shifted heavily or died (Winn, Dukat, Damar, Weyoun, Rom, Leeta, etc).
Relaunch begins. Introduce Vaughn, Shar, Prynn, Sam, (re-introduce) Ro, bring on new background players, sideline Jake. No sign of Sisko, O'Brien, Worf, Odo, Garak, etc.
Huzzah, new crew! Kira, Vaughn, Dax, Bashir, Nog, Shar, Prynn, Sam, Ro, Quark, plus background.
Since then? Shar's been sidelined, status unknown. Major Cenn has been added to the "main" cast. O'Brien, Odo, Garak have guest-starred, but not come back. Sisko's back, but a minor/guest player; same with Jake.
Huzzzah, slight shakeup! Same basic crew as above, just delete Shar and add Cenn.
Now though? DS9's jumping up to "Destiny"'s timeline. We know for sure Dax and Sam (plus some background characters) are gone.
Sooo... huzzah, shakeup!