After completing his teacher training in 1978, Greedy was able to move to the Sydney area to pursue a soccer career.[3] Over the next four years, he played semi-professionally in the New South Wales State League for Bankstown and Melita Eagles.[1] Melita coach Attila Abonyi recommended Greedy to his former club St George Saints, where Abonyi's friend and former teammate Frank Arok was coach. Greedy subsequently signed for St George and became a top-flight player in the National Soccer League (NSL) at the age of 27.[3] He played in the NSL for St George from 1982 to 1986, winning the league in 1983, and for APIA Leichhardt in 1988.[4][5]
Following Arok's appointment as the coach of the Australian national team in 1983, Greedy was called up to the squad for a series of matches against the touring England team in June that year, making his international debut in the first match of the series at Sydney.[3] He was the first choice goalkeeper over the next two years, including the qualifying matches for the 1986 World Cup. After winning the Oceania qualifying group, Australia faced Scotland in a two-legged play-off to qualify for the finals, but lost 2–0 on aggregate. According to Greedy, he chose to retire from the national team after these matches on a point of principle following a dispute over money between the players and the national federation.[3][6][7][8][9]
Despite his brief international career, Greedy was later named in the Socceroos Team of the Decade for the 1980s.[3] He made 16 full international appearances and – including unofficial matches against club teams – played for Australia 36 times in total. He also played for New South Wales state representative teams.[1]
