Cleary was born in Dover Heights, New South Wales and was educated at Waverley College. In 1943 having initially lived in Hardy street, his family moved to 17 Rodney Street, Dover Heights, where his father had built a new family home. At age 17, having set a number of schoolboy sprint records, he was offered a sporting scholarship to Stanford University, which he declined, with his sights set on representing Australia in athletics.

In 1959 he joined the Randwick DRUFC and played in the club's 1960 winning first-grade premiership side. He was selected in the Australian national side for all three Tests of the 1961 series against Fiji and made further Wallaby appearances against France, and against the Springboks on the 1961 tour of South Africa.

After leaving rugby union, during his first year of rugby league with the South Sydney Rabbitohs, Cleary maintained his amateur status to enable his selection for the Commonwealth Games later that year. He represented Australia in athletics at the 1962 British Empire and Commonwealth Games in Perth, placing third in the 100-yard sprint. He recorded 9.3 secs for the 100 yards during his athletic career.^[3]

In 1964 he beat the rugby league speedster Ken Irvine in a A£2,000 match race at Wentworth Park, and in 1966 he won the Australian professional 130m sprint race.

Cleary joined the South Sydney Rabbitohs in 1962 along with Jim Lisle his Wallaby three-quarter partner. Cleary was a Winger with the club throughout the 1960s playing in three premiership winning sides in 1967, 1968 and 1970. Cleary finished his first grade career with the Rabbitoh's neighbouring club, the Eastern Suburbs Roosters, in 1971. This made him ideally suited to represent his future NSW State electoral district of Coogee, which sits close to the geographic border between the two clubs.

His international rugby league debut in the 1st Test against Great Britain in Sydney on 9 June 1962 saw Cleary become Australia's 29th dual-code international, following Arthur Summons and preceding Jim Lisle. He made Test appearances against New Zealand in 1963, 1965 and 1969; against France in 1964 and was selected for the 1963–64 Kangaroo tour of Great Britain and France^[4] during which he made one Test and twenty tour match appearances.

He is one of only four Australian sportsmen to represent internationally in three different sports at the senior level (see also Dick Thornett and Snowy Baker).

Cleary joined the Labor Party in 1965 and was the State member for Coogee in the New South Wales Legislative Assembly from 1974 to 1991 and was the NSW Minister for Sport and Recreation and Tourism in the Wran Labor Government from 1981 to 1988. From 1986 to 1988 he was also the NSW Minister for Racing.^[5]

He was at one time or another the Chairman Sports House Advisory Committee, member North Bondi Surf Life Saving Club, member Coogee Surf Life Saving Club and a director South Sydney Leagues Club.

In the Queen's Birthday Honours list of 1992, Cleary was awarded an Officer of the Order of Australia for his service to the New South Wales Parliament,^[6] and in 2000 he was awarded the Australian Sports Medal for his achievements as a Kangaroo player.^[7] He was inducted into the Sport Australia Hall of Fame in 1999.^[2]

Cleary was a wrestling commentator for World Championship Wrestling.^[8][9]