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.

[2] On 4 August 2016 it was announced that Klimavičius signed with Neptūnas Klaipėda of the Lithuanian Basketball League.

[3] 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.

At the 2010 FIBA World Championship he played for the Lithuanian national basketball team, which won Bronze medals.