Beverley played from 2006, two years for the Razorbacks called university team from the University of Arkansas. Then he left the university to play in Europe. The first club for Beverley was from the 2008/09 season the club Dnipro Dnipropetrovsk in the Ukrainian Basketball League. This season, he came up with a points average of 16.7 per game.
Although in the second round of the NBA Drafts 2009 selected by the Los Angeles Lakers, Beverley remained in Europe and signed a contract with Olympiakos Piraeus. With Piraeus he reached to the side of Josh Childress and Linas Kleiza the Final Four in the ULEB Euro Cup 2009/ 10 where the team was defeated by FC Barcelona in the final. In the same year Piraeus won the Greek Cup and reached the second place in the Greek championship.
Beverley moved to the Cup win in Greece in January 2011 to the Russian club Spartak Saint Petersburg. After moving to Spartak Saint Petersburg, he won with his new team the Russian Cup and reached the Final Four in the FIBA Euro Challenge. In the season 2011/2012 Beverley was named MVP of the regular season of the Euro Cup. He was also MVP of October 2011 in the VTB United League. In December 2012, he left the Russian team after almost two years.
On January 7, 2013 Beverley signed a contract with the Houston Rockets in the NBA. First briefly for their farm team, the Rio Grande Valley Vipers, active, he was on 15 January his NBA debut for the Rockets.
In the FIBA U19 World Championships 2007 in Novi Sad Beverley labeled with the team of USA 2nd place.