Career
He was drafted by the Senators in the fifth round (126th overall) of the 2011 National Hockey League draft. Claesson began playing hockey in Haninge The Human Context, and later moved on to Hammarby IF, to play in Hammarby"s youth organization. He also made two appearances in the club"s senior team in the Swedish second division league HockeyAllsvenskan, during the 2007-2008 season.
Claesson moved to Stockholm rival Djurgården for the 2008-2009, where he played in Djurgården"s J18 and J20 teams.
He also represented team Stockholm at the 2008 television-pucken. Claesson made his Elitserien debut in the Djurgården"s first league game of the season on 16 September 2010 against HV71.
He signed a two-year extension with Djurgården in October 2010. He scored his first Elitserien goal on 11 December 2010 away against Modo Hockey.
Claesson signed a three-year entry level contract with the Ottawa Senators on May 10, 2012.
He began the 2012-2013 season with the Senators American Hockey League affiliate, the Binghamton Senators. In June 2015, Claesson re-signed with the Senators on a one-year, two-way contract. Claesson made his National Hockey League debut on December 30, 2015 at Ottawa versus the New Jersey Devils.