Career
On the 17th of February, it was revealed on the Hearts website that he was having a trial with the Scottish Premier League side. On 8 December 2009 the 27-year-old Lithuanian defender has signed a two year deal with Sibir. In 2011 he signed for Kazakhstani side Football Club Zhetysu.
In December 2014, Klimavičius moved to Football Club Tobol.
Klimavičius played 8 games at Union of European Football Associations Euro 2008 qualifying.