Klimavičius played for BC Žalgiris, BC Alita, Fabriano Basket early in his career, before having breakout seasons with BC Šiauliai, helping them win LKL bronze medals in 2006 and 2007, BBL bronze medals in 2006, and helping Šiauliai in FIBA EuroChallenge competition. After a successful season G.S. Olympia Larissa B.C., Klimavičius returned to Žalgiris Kaunas. After a difficult 2008-2009 season for the team, Klimavičius played his most successful season with Žalgiris, becoming one of the best players on the team, and helping the team in matches in the Euroleague and against BC Lietuvos rytas, winning the BBL championship in 2010.
Klimavičius has signed a new contract and will stay with Žalgiris Kaunas for 2010–2011 season, with an option to prolong the contract for the 2011–2012 season.[1] In 2014, Klimavičius signed with Telekom Baskets Bonn of Basketball Bundesliga.[2]
On 24 January 2017 Klimavičius signed with Vytautas Prienai-Birštonas shortly after terminating his contract with Neptūnas. He became an important part in the Vytautas rotation, and helped the team to win the 2017 BBL championship. He left Vytautas in January, after suffering some injuries.