A speedy winger, Tony Graham started his career at the Cronulla-Sutherland Sharks in 1976. The following year Tony Graham was awarded a two-year contract with the St. George Dragons and joined the 'Bath's Babes' squad, overseen by the mastercoach, Harry Bath. He started off 1977 in first grade, but eventually lost his place in the team to the emerging talent of Stephen Bulter. Although Graham was a reserve back for the 1977 Grand Final, his later appearances for the club were mostly in the reserve grade team.
Tony Graham returned to the Cronulla-Sutherland Sharks for one last season in 1980, and then retired.[1]