A tall fast-medium bowler, able to swing the ball either way,[1] Drennan made his first-class debut in the 1953-54 season, taking 17 wickets for South Australia in the Sheffield Shield at an average of 32.88.

He took 6 for 82 against Queensland in 1955-56[7] and played in a trial match that was held to help the national selectors choose the team for the tour of England in 1956.

[13] But in the second innings of the match against Eastern Province shortly before the First Test, he broke down in his 11th over, tearing a hamstring muscle[1] after taking 3 for 25.

[1] In 1960 he played as the professional for Rishton in the Lancashire League, taking 81 wickets at 13.05 and scoring 430 runs at 19.55.

[1] Drennan married Eril Homburg, a basketballer for the Australian women's team in the 1957 World Championship.