^There's a good deal of Trek fiction that isn't about familiar characters and settings, that adds new characters and worlds and storylines to the universe and that might suit your interests better. The seminal example is The Final Reflection
by John M. Ford, which is supposedly a work of historical fiction written within
the Trek universe about events occurring several decades before the original series, as told from a Klingon perspective. It's not consistent with modern screen continuity, but it's a terrific piece of worldbuilding and stands as a solid original SF novel in its own right.
More recently, we've had a bunch of series about non-screen characters, including New Frontier, Titan, SCE/Corps of Engineers, Vanguard
, and Department of Temporal Investigations