Drewett won in 1975 and 1977 the junior title at the Australian Open. In 1981, he won by the side of Erik van Dillen his first of seven double tournaments on the ATP World Tour. In 1982 he won in Cairo his first of two individual titles, he stood four more times in a final. Its highest listing in the tennis world ranking he reached in 1984 with position 34 in the singles and in 1988 with position 18 in doubles.
His best individual result at a Grand Slam tournament was reaching the quarterfinals at the Australian Open in 1976, which he won twice in the junior competition. In the doubles competition, he reached the semi-finals in each of the Australian Open on the side of Marty Davis in 1988 and 1989.
Drewett was appointed in 1980 a single time in the Australian Davis Cup team and played in the 5-0 victory against Japan, the double game on the side of Mark Edmondson. Though they won the game, he is no longer included in the sequence.
Drewett was married and had two children. After the end of his professional career, he became self-employed as a businessman, he also worked as a commentator for the Australian television station Channel 9 worked. Between 1999 and 2003, he was Executive Vice President, since 2006, he was Chief Executive Officer of ATP. He was also a finals tournament since 2001 director of the ATP World Tour. From the beginning of 2012 was Drewett Chairman and Chief Executive Chairman of ATP.
In Drewett on January 14, 2013 Amyotrophic lateral sclerosis (ALS, also known as Lou Gehrig 's disease and Charcot 's disease) was diagnosed. He died on 3 May 2013.