Claver began his playing career with the youth teams of his school, Sagrado Corazón HH.

He also played in the European top-tier level, EuroLeague, during the 2010–11 season, and averaged 10.9 points and 4.9 rebounds, over 14 games.

On 19 February 2015, Claver was traded, along with Will Barton, Thomas Robinson and a lottery-protected 2016 first-round pick, to the Denver Nuggets in exchange for Arron Afflalo and Alonzo Gee.

[8] On 2 September 2015, the Russian team Lokomotiv Kuban announced a one-year deal with Claver for the 2015–16 season.

[11] On 20 July 2016, he signed a three-year deal with FC Barcelona Lassa, after his new team reached an agreement with Valencia for acquiring his rights.

[citation needed] He also played at the 2010 FIBA World Championship, the 2014 FIBA Basketball World Cup, at the 2012 Summer Olympics, where Spain won a silver medal, and at the 2016 Summer Olympics, where Spain won a bronze medal.