Just a collection of ideas from various threads...
First, the timeline
. I suggest the story take place circa 2450 CE, roughly 75 years after TNG. However, we deliberately refrain from any explicit statement about which timeline counts as "history." This in effect translates as zero references to the planets Vulcan, New Vulcan or Romulus and we resist the temptation to show a lot of Vulcans.
. The starship Enterprise-G
, a huge new vessel with a crew of around 3000. An impressive vessel with primary, secondary and emergency shields. Among its shuttles is the Reliant
, in effect a super-runabout but built to include a "phase-cloak" such as the one attempted with USS Pegasus
. This one works fine, but requires enormous power as well as minimal shields. More, another phased ship's weapons can hurt it.
heads out to a new region of space, in the outer sectors of the Alpha or Beta quadrants, generically known as the Antilles Cluster. Legend among some space-faring civilization say it is the abode of Gods. Or Demons. Or both.
. Focus on a group of four or five very promising Ensigns. Some are friends, others rivals. Maybe a young lady by the name of Kirk, trying to live up to her family's long shadow. And an alien we haven't seen before, one hopefully with as rich a background as the Cardassians. All of these young officers tend to end up on Away Teams, and one is a particularly excellent pilot. Another a gifted medic. They see the Captain now and then, but more usually interact with the First Officer, Science Officer, Chief Engineer and Chief Medical Officer.
Fourth, story arc
. The Antilles Cluster is home base to a League of different alien races, many disturbing if not disgusting to most humanoids. The League was founded by a race of Patrons, roughly on the same evolutionary level as the Metrons or Excalbians. But the Patrons, while revered, in fact rarely intervene and when they do their actions are often baffling (the Starfleet folk know none of this initially).