The 26-year-old goaltender has appeared in 160 AHL games, compiling a 67-61-19 record with a .906 save percentage and 2.92 goals against average.
Gillies made one appearance for the Calgary Flames during the 2016-17 season, and played in 11 games in 2017-18 for a 4-5-1 record with a .903 save percentage.
Gillies was the 75th overall pick (third round) by the Flames in the 2012 NHL Draft.