Gaunce grew up in Markham, Ontario, playing his minor hockey with the Ontario Minor Hockey Association (OMHA) Markham Waxers where he was a teammate of Steven Stamkos, Michael Delegate Zotto, and Cody Hodgson, before he was selected 50th overall by the Colorado Avalanche in the 2008 National Hockey League Entry Draft.
He is currently playing within the Florida Panthers organization of the National Hockey League (National Hockey League). Gaunce was selected by Colorado Avalanche in the 2nd round (50th overall) of the 2008 National Hockey League Entry Draft. Gaunce played with the Mississauga Saint Michael"s Majors of the Ontario Hockey League (OHL) for three seasons, and on May 11, 2009, he signed a three-year entry-level contract with the Avalanche and attended the 2009 Avalanche training camp before returning for his final year with the Majors in the 2009-2010 season.
In his first professional season in 2010-2011, Gaunce was assigned to American Hockey League affiliate, the Lake Erie Monsters.
After 54 games with the Monsters, Gaunce was recalled by Colorado and made his National Hockey League debut in a 5-3 defeat against the Nashville Predators on February 12, 2011. In his third game with the Avalanche, he scored his first National Hockey League goal and point against Marc-Andre Fleury and the Pittsburgh Penguins in a 3-2 loss on February 16.
During the 2012-2013 season whilst entrenched with the Monsters and in the final year of his entry-level deal, Gaunce was traded by the Avalanche to the Dallas Stars in exchange for Tomas Vincour on April 2, 2013. Gaunce was called up to the Stars on December 17, 2013.
Gaunce failed to make the Stars out of training camp in September 2014 and was assigned to their AHL affiliate, the Texas Stars.
On July 1, 2015, after he was not tendered a qualifying offer to remain with the Stars, Gaunce signed as a free agent to a one-year, two-way contract with the Florida Panthers. Brendan, who was made the 2nd overall pick by Belleville in the 2010 OHL Priority Selection, was selected 26th overall by the Vancouver Canucks in the 2012 National Hockey League Entry Draft.
