[1] Carrier was selected in the fourth round, 61st overall at the 2010 Quebec Major Junior Hockey League (QMJHL) draft by the Cape Breton Screaming Eagles.

[6] During a game against the Baie-Comeau Drakkar, Hockey Canada’s head scout Kevin Prendergast attended to view Carrier's play.

[12] During a game against the Boston Bruins in December 2016, Carrier was penalized for an illegal check to the head on David Backes, who suffered a concussion.

During the first round of the playoffs against the Los Angeles Kings, Carrier entered into concussion protocol as a result of an illegal check to the head by Drew Doughty.

[17] By the 2022–23 season, Carrier was one of six remaining original members of the Golden Knights, alongside Jonathan Marchessault, William Karlsson, Reilly Smith, Brayden McNabb and Shea Theodore.

[18] Following seven seasons with the Golden Knights, Carrier left the organization as a free agent and was signed to a six-year, $12 million contract with the Carolina Hurricanes on July 3, 2024.