After a breakthrough campaign during the 2011 Superettan season, Claesson join IF Elfsborg in the Allsvenskan, the top division of Swedish football.

On 25 January 2017, Claesson signed a 3.5-year contract with Russian Premier League team FC Krasnodar.

[8] Out of action for over 14 months, Claesson returned from injury on 18 August 2020, playing the last 15 minutes of Krasnodar's 2–0 home win over Arsenal Tula in the Russian Premier League.

[9] Four days later, Claesson scored from the penalty spot in the club's first-leg play-off round match against PAOK for qualification to the group stage of the UEFA Champions League.

[10] Krasnodar would win the second leg against PAOK by the same scoreline and secure progression to the group stage of the Champions League for the first time in the club's history.