Claver began his playing career with the youth teams of CD Maristas and Pamesa Valencia (Valencia BC since 09-10) in Spain. He made his professional debut with Valencia BC's farm team, Valencia BC 2, during the 2004–05 season. He moved up to the Spanish ACB League for the first time during the 2006–07 season, when he debuted with the senior team of Valencia BC. He played in Europe's second-level competition, the ULEB Cup, for the first time during the 2007–08 season.
Winner of the Slam Dunk Contest of ACB League in 07-08 season.