The Faded Sun Trilogy (Kesrith, Shon'jir, Kutath)

From the back cover:

This is the story of three people: Sten Duncan, a soldier of humanity; Niun, last warrior of the mri, humanity's enemies; Melein, priestess-queen of the final fallen mri stronghold.

This is the story of two mighty species fighting for a galaxy: humanity driving out from Earth, and the enigmatic regul struggling to hold their stars with mri mercenaries.

This is a story of diplomacy and warfare, of conspiracy and betrayal, and of three flesh-and-blood people who found themselves thrown together in a life-and-death alliance.