Trivia Time: Hitmonchan learns the most increased priority moves through level up out of all Pokemon, with six in total: Mach Punch, Bullet Punch, Vacuum Wave, Detect, Pursuit (when switch out), and Quick Guard.
Don't forget Fake Out(atleast as a Tyrouge). So yeah, priority a plenty. And once you leave Hitmonchan, try out Double-Priority (Fake out and Bullet Punch) Normal Gem Unburden Hitmonlee.