I've had a very rough idea of what a post-Voyager/Nemesis show could be like for awhile now. Like I said, very rough, but here are my thoughts using some stuff from the Destiny novels as a springboard...
Setup
2381
The destruction of two planets is followed by a message.
“We are the Borg. You will be annihilated.”
Continuing attacks soon lead to a full scale Borg Invasion into the Alpha and Beta Quadrants resulting in the Federation entering into a multi-world alliance to battle them.
As the Borg attack planet after planet, ships from the Federation Alliance are sent to prevent the attack and destruction of an Independent world on the fringes of Federation space.
Adelphous IV
Shortly after Voyager’s return from the Delta Quadrant, this has been the location of a top secret joint project between the Federation, Klingon Empire, Romulan Star Empire, and Cardassian Union to develop a prototype ship to use against the Borg.
Unfinished, the prototype ship is unable to assist in fending off a calculated Borg attack and the fleet is nearly destroyed.
Before the Borg cubes are able to destroy the world, an anomaly appears and the planet begins to disintegrate. The planet, surviving ships, and debris of the destroyed are sucked into the anomaly.
Unknown Galaxy
Adelphous IV reforms in orbit of a class K star in a galaxy beyond the known universe, along with ships and debris in orbit.
Some debris from wrecked ships is caught in the planets gravity as it reforms and rains down to the surface creating a ship graveyard planetside along with the one in orbit.
Surviving ships are heavily damaged and require varying amounts of repair to be operational, limiting travel to only shuttles.
For the most part, everything on the surface survived undamaged.
Series Possibilities
The mystery of the anomaly and who or what is responsible for it is at the forefront of the first season. They have hope of finding a way home but it is tempered with the realization they could be stuck there forever.
The damaged ships limit the exploration to the range of working shuttles.This instills an urgency to repair the ships. There is also the possibility of the prototype ship that is near completion in a construction facility beneath the planet's surface.
The mixture of powers on an independent world creates a possible struggle for power. What shape will a new government take? What would a new federation look like as it raises from a memory of the one that came before?
What inhabited worlds are nearby? If any, they offer a chance for assistance if not hostile. What technology may they offer and will it be accepted/traded for or will the idea of a Prime Directive survive?
Summed Up
A story about the people on this planet who've been blasted into some unknown reality and whom are struggling to decide what to do and how to survive. Let them be like the audience, wondering what the hell happened that got them there. Some characters will be trying to piece together an answer to what happened and how to get back, while others will accept the hand they've been dealt and decide they have to figure out how to live with each other in this forbidding new place. These two groups can have conflicting goals over limited resources (we have to use these ships to build a means to get home vs. we have to use these ships to build a means to defend ourselves or build a new civilization).
One World, One Ship, An Unknown Galaxy, A New Federation