Referenced in a couple of behind-the-scenes documents from the making of Star Trek: The Original Series, a trump card is, in many trick-playing card games, a playing card of a suit that has been chosen to outrank all other suits.
In a stage direction from the final revised draft script of "The Conscience of the King", Lenore Karidian was referred to as playing her trump card when she offers for the Karidian Company of Players to stage a play onboard the USS Enterprise in exchange for safe passage to Benecia.
In the story outline for "Turnabout Intruder", Janice Lester (then called "Janice Lisette"), in the body of James T. Kirk, was described as playing her trump card with Dr. Coleman by promising to make him the Enterprise's surgeon if he secretly helped her execute Kirk, who was meanwhile occupying Janice's body.