Gleeson was first player selected to represent Queensland in 1961 against New South Wales.
[2] In 1963, Brisbane Rugby League club Wynnum signed a host of big-name players, including Gleeson.
After helping Brothers to the 1967 Brisbane Rugby League premiership,[7] he went on the 1967-68 Kangaroo tour.
With Gleeson filling in for the injured Billy Smith at halfback, fellow Queenslander Peter Gallagher led a depleted Australian team to an upset series victory.
[8] In 2008, rugby league in Australia's centenary year, Gleeson was named on the bench of the Toowoomba and South West Team of the Century.