Rogue Captain Brad Majors, CO of the stolen ship StarSlayer (formerly USS Dominant), is a PNPC owned by Lt. Cmdr. Anthony Clifton (USS Odyssey).
The StarSlayer is a former Federation starship (USS Dominant) that was commandeered by Brad Majors, her Exec when he deemed Starfleet was double crossing his former captain. He basically turned the ship into a pirate vessel, and made his way via a stolen quantum slipstream to the Delta Quadrant (among other places).
Majors was becoming disillusioned with Federation hypocrisy as he saw it, and that pushed him over the edge. A small group stayed with him, but most of his crew are whoever or whatever joined him over the last 2 years. He has been stealing tech wherever he could for this ship, and is now heavily modified and armed, with a wide array of alien technology.
Despite the fact that he now prefers to live as an outlaw, he is still loyal to the Federation. He may be a pirate but he would not help anyone hurt the Federation.
Upon returning to the Alpha Quadrant he helped Odyssey crew deal with a dangerous situation, but he also tried wooing Exec Jo MacLaren (who rejected his advances).
See Odyssey Mission: ‘Meanwhile in outer Space’
At the end of that mission Majors returned to his ship to discover that Vlak (a Kazon) had organized a mutiny against him and was intent upon taking over the ship.