Claesson played six seasons in the Senators organization, but the majority was with Binghamton of the American Hockey League. He did not land in the NHL full-time until 2017-18, when he scored seven points (one goal, six assists) in 64 games. He was not tendered a qualifying offer after the season and became an unrestricted free agent.

Claesson signed a three-year, entry-level contract with the Ottawa Senators on May 10, 2012 after they selected him in the fifth round (No. 126) of the 2011 NHL Draft.

Claesson signed a three-year, entry-level contract with the Ottawa Senators on May 10, 2012 after they selected him in the fifth round (No. 126) of the 2011 NHL Draft.

Claesson played six seasons in the Senators organization, but the majority was with Binghamton of the American Hockey League. He did not land in the NHL full-time until 2017-18, when he scored seven points (one goal, six assists) in 64 games. He was not tendered a qualifying offer after the season and became an unrestricted free agent.

Claesson signed a one-year contract with the New York Rangers on July 1, 2018. He played 37 games for New York in 2018-19 and scored six points (two goals, four assists). Claesson again became a free agent after the season and signed a one-year contract with the Carolina Hurricanes on Sept. 17, 2019.

After 47 games with Charlotte of the American Hockey League, Claesson was traded by the Hurricanes to the Devils on Feb. 24, 2020. He scored two points (one goal, one assist) in five games for New Jersey before the NHL season was paused March 12 due to concerns surrounding the coronavirus.

On the international stage, Claesson helped Sweden win the 2012 IIHF World Junior Championship.

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