Carey was drafted by the Colorado Avalanche in the 5th round, 135th overall, in the 2007 NHL Entry Draft. Carey played two years at Salisbury School in Connecticut before moving on to compete in the United States Hockey League with the Indiana Ice in the 2007–08 season and was a Rookie of the year finalist, before committing to play for the Boston College Eagles of the Hockey East in his freshman year in the 2008–09 season. After capturing his first national title with the Eagles in his sophomore year, Carey repeated the feat in his senior year in 2012, scoring the championship winning goal against Ferris State University and earning selection to the Frozen Four All-Tournament team. Carey was subsequently signed by the Avalanche to a two-year entry level contract on April 11, 2012. He was immediately assigned on an amateur try-out to begin his professional career and finish the duration of the season with AHL affiliate, the Lake Erie Monsters. He made his professional debut in a 5–3 victory over the Hamilton Bulldogs on April 13, 2012. In his first full professional season in 2012–13, Carey was an offensive contributor for the Monsters. After scoring his first professional goal and point against the Oklahoma City Barons, on October 13, 2012, Carey played in 72 games to finish fourth amongst Lake Erie players with 19 goals and 41 points. During the season, Carey accounted for the team's longest individual point scoring streak at 8 games. During the following 2013–14 season, despite a dip in his offensive numbers, Carey received his first NHL recall by the injury depleted Avalanche on March 11, 2014. He made his NHL debut with the Avalanche in a 3–2 victory over the Chicago Blackhawks on March 12. Carey was assigned to the Lake Erie Monsters to begin the 2014–15 season. Amongst the top offensive producers on the Monsters, Carey was recalled by the Avalanche on multiple occasions and on February 15, 2015, in his 17th career game he recorded his first NHL point, an assist, in a 5–2 victory over the Arizona Coyotes. On March 2, 2015, Carey was traded by the Avalanche along with Maxime Talbot to his hometown team, the Boston Bruins, in exchange for Jordan Caron and a 6th-round draft pick in 2016. On July 8, 2015, Carey signed as a free agent to a one-year, two-way contract with the Washington Capitals. He scored his first NHL goal on February 6, 2016, against Cory Schneider of the New Jersey Devils while playing in his third game for the Capitals. He was called up a day earlier for the second time of the season by the Capitals from the American Hockey League, where he was playing for the Hershey Bears. After two seasons within the Capitals organization, Carey left as a free agent to sign a one-year, two-way contract with the New York Rangers on July 1, 2017. After enjoying a solid training camp and pre-season with the Rangers, and with Jesper Fast injured, Carey was named on the opening night roster to begin the 2017–18 seasonfor the first time in his career. Carey was initially a healthy scratch before drawing into the lineup in a depth role. In contributing defensively and showing a two-way game, Carey set career markers of 7 goals and 14 points in 60 games for the Rangers in completing his first full season in the NHL. As a free agent in the following off-season, Carey left the Rangers to sign a one-year, two-way contract with the Ottawa Senators on July 1, 2018. After participating in the Senators 2018 training camp and pre-season, Carey remained on the opening roster for the 2018–19 season. He made debut in helping the Senators claim their first win of the campaign in a 5–3 decision over the Toronto Maple Leafs on October 6, 2018. Carey was scoreless in 5 games for Ottawa before he was placed on waivers and sent to AHL affiliate, the Belleville Senators, on October 24. After 29 games in Belleville, Carey was traded by Ottawa and acquired for a second time by the Boston Bruins in exchange for Cody Goloubef on January 11, 2019. He was assigned to continue in the AHL with the Providence Bruins. On March 26, Carey signed a two-year, two-way contract extension with the Bruins.
