He was a member of the International Panel of ICC Umpires between 2003 and 2008.
His first match was between Australia and New Zealand at Brisbane on 3 December to 7 December 1993, won by Australia by an innings and 96 runs, with Allan Border and Steve Waugh scoring centuries, and Shane Warne and Craig McDermott taking 8 and 6 wickets respectively.
Parker's last Test match in Australia was between Australia and the West Indies at Perth on 1 December to 3 December 2000, won by Australia by an innings and 27 runs with Mark Waugh scoring a century, and wickets being shared by Glenn McGrath (who took a hat-trick), Brett Lee, Jason Gillespie and Stuart MacGill.
Parker's partner was the English umpire John Hampshire.
Parker retired to focus on his career away from the game in October 2008.