Gélinas began playing ice hockey at the age of four, and modelled his game after Chris Pronger, from whom he took the jersey number 44. At the major junior level, Gélinas played two seasons for the now-defunct Lewiston Maineiacs of the Quebec Major Junior Hockey League, and in 2008–09 led team defencemen in points, registering ten goals and 29 assists in 67 games. He also participated in the 2009 CHL Top Prospects Game. At the end of the season, on June 26, 2009, he was drafted by the New Jersey Devils in the second round, 54th overall, at the 2009 NHL Entry Draft. Following the Maineiacs' folding in 2011, Gélinas played one-and-a-half seasons for the Chicoutimi Saguenéens before eventually being traded to the Saint John Sea Dogs. He was then part of the Sea Dogs team that won the 2011 Memorial Cup, defeating the Mississauga St. Michael's Majors in the final.
Professional
Upon finishing his major junior career, Gélinas was assigned to the Albany Devils, New Jersey's affiliate in the American Hockey League. He played in 75 games during the 2011–12 season, tying the AHL lead in goals by a defenceman with 16, while being named top Albany defenceman and finishing 16th overall in the League in points for a defenceman, with 37. In the following season, 2012–13, Gélinas missed nearly two months of action after taking a puck in the mouth during Albany's final pre-season game at the Binghamton Senators on October 6, 2012; the impact left him with a broken lower jaw. After returning from the injury, Gélinas played 57 games, scoring six goals and 16 assists for 22 points. On April 23, 2013, Gélinas was called up from Albany to join the New Jersey Devils. He made his NHL debut at the Devils' last home game of the 2012–13 season against the Pittsburgh Penguins. In the 2013–14 season, he scored his first NHL goal on October 24, 2013, against Roberto Luongo of the Vancouver Canucks. Following the 2014–15 season, Gélinas became a restricted free agent under the NHL Collective Bargaining Agreement. The New Jersey Devils made him a qualifying offer to retain his NHL rights and, on July 5, 2015, Gélinas filed for salary arbitration. In the 2015–16 season, Gélinas was traded at the trade deadline to the Colorado Avalanche in exchange for a 2017 3rd-round pick on February 29, 2016. On June 26, 2017, Gélinas as an impending restricted free agent, was not tendered a qualifying contract by the Colorado Avalanche, thus ending his tenure with club in releasing him to free agency. On August 29, 2017, Gélinas signed with the Montreal Canadiens to a professional tryout contract, where he would attend the team's training camp. Gélinas was not given a contract by the Canadiens, but was signed by the team's AHL affiliate, the Laval Rocket on October 1. In the 2017–18 season, Gélinas regained his scoring touch from the blueline with the Rocket, contributing with 13 goals and 26 points in 64 games as Laval missed out on the playoffs in their inaugural season. As a free agent in the off-season and unable to attract a NHL contract, Gélinas opted to pursue a contract abroad, agreeing to a one-year deal with Slovakian club, Slovan Bratislava of the Kontinental Hockey League on August 23, 2018. In the 2018–19 season, Gélinas established himself with Slovan in a top four pairing role on the blueline, recording 5 goals and 15 points in 52 games. With Slovan eliminated from playoff contention, Gélinas left the club with 3 game left in the season to join Swedish outfit Rögle BK of the SHL, for their post-season push on February 17, 2019.
