Graeme began his career with Wollongong in 1961. Graeme played 2 seasons for Wollongong. In 1963, Graeme joined the St George Dragons. Graeme was a part of St George’s Grand final victories from 1963-66. Graeme was captain-coach of St. George from 1972-1976. Graeme led St George to the 1975 Grand Final. Graeme retired early in 1976. Graeme played 229 games for St George over 14 seasons (87 tries, 648 goals).
In 1962 Graeme represented Country Firsts. Graeme played 6 games for City Origin from 1967-73 (5 tries, 32 goals). Graeme played 33 games for New South Wales from 1962-75 (19 tries, 40 goals). Graeme was captain-coach of New South Wales from 1973-76. Graeme played 45 test matches for Australia from 1963-75 (21 tries, 71 goals). Graeme was captain-coach of Australia from 1973-75.
Graeme was the NSWRL top point scorer in 1971 and 1973. In 1976, Graeme was made a Member of the Most Excellent Order of the British Empire (MBE). In 1999, Graeme was selected as the 5th Immortal. In 2002, Graeme was inducted into the Australian Hall of Fame. In 2008, Graeme was selected for the Australian Team of the Century on the Bench. Also in 2008, Graeme was selected s a centre in the New South Wales and Country Teams of the Century. In 2008 Graeme was named one of Australia’s 100 Greatest Players. In 2010, Graeme was selected as fullback in the Illawarra Team of the Century. In 2017, Graeme was inducted into the NSWRL Hall of Fame. In 2018, Graeme was inducted into the NRL Hall of Fame.
Graeme passed away on January 20 2018.