Largely known for his successful tenure at WIT Georgia, in the late 2000s Klimiashvili was a member of the national team as well.

As a footballer, Irakli Klimiashvili grew up at WIT Georgia, one of the most decorated Georgian teams in the first decade of XXI century.

He made his debut for Georgian national team on 27 May 2008 in a 1–1 friendly game against Estonia as a substitute.

[2] Later he featured in four more matches, including in a UEFA World Cup qualifying game against Montenegro.

In 2013, Klimiashvili joined the Latvian side Skonto Riga, which came 2nd both in the league and Cup competitions this season.