Traveller: New Rome
This is a setting intended for the Traveller RPG, specifically the Mongoose Traveller RPG, though it’s probably suitable for any edition of the game with a little fudging.
The high concept is that future Earth, through a series of wars and schemes, has ended up re-adopting old Roman political and military ideas. Having invented technology that allows FTL “jump” travel to nearby star systems, New Rome is set on a mission to explore and colonize every world it can reach. Of course, New Rome will bring its own civilization, religion, culture, science, law, and government to these places, and as it turns out, almost every world they reach seems to be filled with people—mostly pre-star-travel people. Those pre-jump civilizations are easily conquered, but the Republic is stretched thin and a shortage of jump ships means that small vessels are being sent to the borders of known space with explore-and-conquer missions.