Gaunce grew up in Markham, Ontario, playing minor ice hockey with the Ontario Minor Hockey AssociationMarkham Waxers, where he was a teammate of Steven Stamkos, Michael Del Zotto and Cody Hodgson. He played in the 2003 Quebec International Pee-Wee Hockey Tournament with Markham. He was selected 50th overall by the Colorado Avalanche in the 2008 NHL Entry Draft. Gaunce played with the Mississauga St. Michael's Majors of the Ontario Hockey League for three seasons, and on May 11, 2009, he signed a three-year, entry-level contract with the Avalanche and attended the 2009 Avalanche's training camp before returning for his final year with the Majors in the 2009–10 season. In his first professional season, in 2010–11, Gaunce was assigned to Colorado's American Hockey League affiliate, the Lake Erie Monsters. After 54 games with the Monsters, he was called-up to the NHL and made his NHL debut in Colorado's 5–3 defeat against the Nashville Predators on February 12, 2011. In his third game with the Avalanche, he scored his first NHL goal and point against Marc-André Fleury and the Pittsburgh Penguins in a 3–2 loss on February 16. During the 2012–13 season, while playing with the Monsters and in the final year of his entry-level contract, on April 2, 2013, Gaunce was traded to the Dallas Stars in exchange for Tomáš Vincour. On December 17, 2013, Gaunce was called-up to the Stars. In September 2014, after failing to make the Stars' NHL roster out of training camp, Gaunce was assigned to Dallas' 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. Gaunce was assigned to add leadership to Florida's AHL affiliate, the Portland Pirates, for the duration of the 2015–16 season. He responded by setting career-high numbers offensively with 37 points in 75 games. On July 1, 2016, as a free agent, Gaunce signed a one-year, two-way contract with the Pittsburgh Penguins. In the 2016–17 season, he began playing in the AHL with the Wilkes-Barre/Scranton Penguins. With Pittsburgh suffering a depleted blueline through injury, Gaunce was recalled and eclipsed his previous efforts in the NHL to record a career-high 1 goal and 4 points in 12 games. On July 1, 2017, as a free agent for the third straight year, Gaunce signed a two-year, two-way contract with the Columbus Blue Jackets. In the 2017–18 season, after attending the Blue Jackets' training camp, Gaunce was reassigned to Columbus' AHL affiliate, the Cleveland Monsters. In making his return to his first professional club in the Monsters, Gaunce added a veteran presence on the blueline and led the defence in scoring with 21 assists and 24 points. On July 1, 2018, Gaunce signed a one-year, two-way contract with the Tampa Bay Lightning.
