Regent is a title which is granted to an individual who rules on behalf of another individual, either because the actual ruler has not reached the correct age to rule, or are either absent or incapable of ruling.
In 2267, a power struggle amongst the Ten Tribes of Capella IV led to the death of Teer Akaar. Akaar's infant son, Leonard James Akaar, was proclaimed Teer as his replacement with his mother, Eleen, acting as regent until he was of age. (TOS episode: "Friday's Child")
In the mirror universe, regent was a title that was held by the ruler of the Klingon-Cardassian Alliance. In the 2370s, the title was held by Worf and Martok. (DS9 episodes: "Shattered Mirror", "The Emperor's New Cloak"; DS9 - Obsidian Alliances novel: Saturn's Children)