He previously played in the National Hockey League (NHL) with the Edmonton Oilers, St. Louis Blues, Nashville Predators, Vegas Golden Knights, Minnesota Wild, Vancouver Canucks and Colorado Avalanche.

Hunt beginning his professional career in the American Hockey League (AHL) with the Chicago Wolves, where he was an All-Star in the 2012–13 season.

[4] As a child Steve, a former Senior AA goaltender, set up a deck for Brad to shoot pucks from in the family's backyard.

[11] In the 2007–08 season, his final with the team, he increased his offensive production to 16 goals and 55 points and played in the BCHL All-Star Game.

[9] His assist total was one shy of tying the school's Division I single season record held by Luke Erickson.

[17] Though they failed to capture the automatic bid for the 2010 NCAA Division I Men's Ice Hockey Tournament, BSU received an at-large bit thanks in part to a school record 22 consecutive weeks of being ranked in the top 15.

[3] He increased his production in the WCHA, scoring 5 goals and 26 points while reducing his penalty minutes (PIMs) to a career low 8.

[7][23][24] Undrafted out of college, Hunt signed an amateur tryout contract with the American Hockey League's (AHL) Chicago Wolves, where his first head coach was Craig MacTavish.

[24] In his first full professional season, Hunt was named to the 2013 AHL All-Star Game, replacing the injured Brett Sterling as the Wolves' representative.

[9][31] In the off-season, Hunt signed a two-year entry-level contract with the Edmonton Oilers, for whom MacTavish had become the general manager.

[37] On July 2, 2016, Hunt effectively made a return to the Chicago Wolves, in agreeing as a free agent to a one-year, two-way contract with the St. Louis Blues.

[39] On July 1, 2017, having left the Predators as a free agent, Hunt agreed to a two-year, one-way contract with expansion club, the Vegas Golden Knights.

[41] He tallied 3 powerplay goals and added 5 points in 29 games from the blueline with the Wild, as the club missed the playoffs for the first time in 7 seasons.

[42] After the better part of three seasons with the Wild, Hunt left the club as a free agent and was signed to a one-year, $800,000 contract with the Vancouver Canucks on July 28, 2021.

[43][44] As a free agent from the Canucks, Hunt was signed to a two-year, two-way contract with the reigning Stanley Cup champions, the Colorado Avalanche, on July 15, 2022.

[45] After attending the Avalanche 2022 training camp, Hunt was placed on waivers and re-assigned to the begin the 2022–23 season with AHL affiliate, the Colorado Eagles.

[48] He was initially named as the Eagles representative to the AHL All-Star Classic, marking his sixth occasion, however remained with the Avalanche.

[52] On May 5, 2023, Hunt was named to Canada men's national ice hockey team at the 2023 IIHF World Championship where he recorded three assists in ten games and won a gold medal.