Claverie was born in Tenerife and his family home as a child was close to a golf course and so his interest in the game was understandable and he first picked up a club at the age of seven. He played golf as a hobby but opted to finish his university degree and, therefore, did not turn professional until he was 26.
Claverie secured his rookie season on the European Tour in 2007 after coming through the Qualifying School at San Roque with the 35th and final card. Despite a disappointing season, he returned to San Roque to Qualifying School and took the fifth available card and regained his card for the 2008 season.
Claverie was twice a runner-up on the Challenge Tour, where he played most of his golf, at the Open Mahou de Madrid and Fred Olsen Challenge de España.