In 1988, after a guest appearance in The Flying Doctors, Fleet took on the role of Dave Summers in the Australian soap Neighbours. His most dramatic sequence in this program involved killing the popular character of Daphne in a car accident. Fleet then appeared in the popular Australian sketch show Full Frontal.
Since then, Fleet has been a regular stand-up comedian around Australia, and has appeared on many TV and radio comedy programs, including The Comedy Channel's Stand Up Australia!. He was the announcer and narrator for the comedy series Real Stories on the Ten Network, and provides the voice of Sandy, the yellow labrador, in TV commercials for the Home Hardware hardware store chain.
Fleet has appeared on The Little Dum Dum Club four times. The first was on the sixteenth episode of the show, which was posted on Feburay 9th, 2011. Greg returned to The Little Dum Dum Club for a live episode at Softbelly Bar in Melbourne with Nick Cody, Virginia Gay, Luke McGregor and Anyone for Tennis? Fleet appeared on episode 87 of the show with Bart Freebairn, in which the two infamously hijacked the show with their absurdism, riffing and improvisations. His most recent appearance on the show came in March 2013 alongside Tony Martin.