An etymology lesson from Tyler Cowen:
trump (v.2) “fabricate, devise,” 1690s, from trump “deceive, cheat” (1510s), from Middle English trumpen (late 14c.), from Old French tromper “to deceive,” of uncertain origin. Apparently from se tromper de “to mock,” from Old French tromper “to blow a trumpet.” Brachet explains this as “to play the horn, alluding to quacks and mountebanks, who attracted the public by blowing a horn, and then cheated them into buying ….” The Hindley Old French dictionary has baillier la trompe “blow the trumpet” as “act the fool,” and Donkin connects it rather to trombe “waterspout,” on the notion of turning (someone) around. Connection with triumph also has been proposed. Related: Trumped; trumping. Trumped up “false, concocted” first recorded 1728.
Note also (from same internal link):
trump (v.1) “surpass, beat,” 1580s, from trump (n.). Related: Trumped; trumping.