Gleeson attended St Patrick's College, Ballarat and later played with St Kilda at Centre half-forward initially. He developed into a skilful and agile ruckman, winning the Brownlow medal in 1957. In the Melbourne evening paper The Herald, 29 August 1957 Gleeson said:
"We are just like a family at St Kilda," he said. "We depend on teamwork and we bring each other into the game. Coach Alan Killigrew is responsible for that and the officials and supporters have given us encouragement and confidence."
Appointed club captain in 1958, he injured a knee in a practice match and never played VFL football again.
Gleeson and 1961 Brownlow Medal winner John James, (who also finished third to Gleeson in 1957), played in the same school team.
