A consort is the spouse of a ruler. More generally, the term refers to anyone who shares the lot of another, but especially a partner or spouse.
In 2366, a Tasha Yar from an alternate timeline returned with the USS Enterprise-C to the battle at Narendra III. The ship was destroyed by the Romulans, and its surviving crew captured. A Romulan general who oversaw their capture became enamored of her and spared the lives of the remaining crew in exchange for Yar becoming his consort. One year later, she gave birth to a daughter named Sela. (TNG: "Redemption II")
In 2371, Seska, an undercover Cardassian operative, was stranded in the Delta Quadrant on board the USS Voyager. In order to get home, she attempted the transfer of Starfleet replicator technology to the Kazon-Nistrim in exchange for their protection but was caught. She escaped aboard a Kazon raider and became the consort of First Maje Culluh, the leader of the Kazon-Nistrim sect. One year later she bore him a son. (VOY: "State of Flux", "Basics, Part I")