Regent was a title given to one who ruled on behalf of another, typically because the actual ruler had not reached maturity, or was absent or infirm.
In 2267, a power struggle fomented by a Klingon agent left Leonard James Akaar as Teer of the Ten Tribes from the time he was just hours old. His mother Eleen ruled as his regent, and signed a mining accord with the Federation. (TOS: "Friday's Child")
Palamar was lead by a regent during the 2370s. (DS9: "Business as Usual") The Evora were led by Regent Cuzar in 2375. (Star Trek: Insurrection)
In the mirror universe, the regent was the ruler of the Klingon-Cardassian Alliance. Worf was the regent in the 2370s. (DS9: "Shattered Mirror", "The Emperor's New Cloak")
Oxilon was the Council Regent of the Talaxians encountered by the USS Voyager in 2378. (VOY: "Homestead")