Klepiš was drafted in the first round, 16th overall by the
Ottawa Senators in the
2002 NHL entry draft. Before ever playing for Ottawa, Klepiš was traded to the
Buffalo Sabres in 2003 in a deal that sent
Vaclav Varada to the Senators. Before ever playing for the Sabres, he was dealt to the
Washington Capitals on March 9, 2004 in exchange for forward
Mike Grier. Klepiš ultimately played in 66 NHL games (all with the Capitals) before returning to Europe to continue his professional career in the
Kontinental Hockey League. He won the
Gagarin Cup in
2012 with
Dynamo Moscow, scoring the series-winning goal in the seventh game. On June 26, 2014, he left
HC Lev Praha after two seasons to join Swedish club, Färjestad BK of the SHL. He then returned to the Czech Republic joining HC Oceláři Třinec before moving to his current club, BK Mladá Boleslav, part way through the 2015/2016 league season. In 2026, it was announced that Klepiš had retired from professional hockey. ==International play==