Cleary was an All-American hockey player at Harvard, starring for two years and setting several team records (many of which still stand) along the way, including most goals in a game (6), longest goal-scoring streak (15), most goals in a season (42) and most points in a single season (89). Cleary's scoring prowess was instrumental in Harvard's invitation to the 1955 NCAA Tournament, the first in school history, and Cleary was named to the All-Tournament First Team after Harvard's third-place finish.