Klesla spent the 1997–98 season with HC Opava Jr. of the Czech RepublicJunior League, where, in 38 games, Klesla scored 11 goals and 29 points. In eight playoff games, Klesla had two goals and four points. Klesla began playing junior hockey in North America in 1998–99, when he played for the Sioux City Musketeers of the USHL. In 54 games, Klesla had four goals and 16 points, while getting 100 penalty minutes. In five playoff games, Klesla scored two goals. Klesla moved to the Brampton Battalion of the Ontario Hockey League for the 1999–2000 season. In 67 games with Brampton, Klesla had 16 goals and 45 points, along with 174 penalty minutes, as he helped the Battalion to their first ever playoff berth. In six playoff games, Klesla had a goal and two points. He returned to the Battalion in 2000–01 season, having a break-out season offensively. In 45 games, Klesla had 18 goals and 54 points. Klesla then added two goals and 11 points in nine playoff games. Klesla also played for the Czech Republic in the 2001 World Junior Hockey Championship, where he had three goals and seven points in seven games.
Professional
Klesla appeared in eight games with the Columbus Blue Jackets in the team's inaugural 2000–01 season, scoring two goals for the team before being sent back to junior hockey with the Battalion. He stayed in the NHL on a full-time basis in 2001–02, scoring eight goals and adding 16 points in 75 games with the Blue Jackets and earning a spot on the NHL All-Rookie Team. After the season, he played for the Czech Republic in the World Hockey Championship, where he had a goal and three points in seven games. Klesla had two goals and 16 points with the Blue Jackets in 2002–03, while scoring two goals and 13 points in a 47 game injury shortened season with Columbus in 2003–04. With the 2004–05 NHL lockout cancelling the season, he played with VHK Vsetín of the Czech Extraliga, where he had seven goals and 24 points in 41 games. Klesla also played with HPK of the Finnish SM-liiga, where he had a goal and three points in nine games, followed by two assists in 10 playoff games with the club. Klesla returned to the Blue Jackets in 2005–06, scoring six goals and 19 points in only 51 games played. After the season, Klesla signed a four-year contract extension with the team. On September 26, 2006, Klesla was suspended for two regular season games for a hit on the Chicago Blackhawks' Tuomo Ruutu in a pre-season game on September 22. Ruutu missed ten games due to a grade two sprain on his knee. Klesla had a very solid 2006–07 season, as he was placed alongside Adam Foote as the Blue Jackets' top defensive pairing after Head CoachKen Hitchcock was hired by the team. In 75 games, Klesla had nine goals and 22 points. In 2007–08, Klesla appeared in all 82 Blue Jacket games, scoring six goals and 18 points. In the off-season, teammate David Výborný left the Blue Jackets, making Klesla the last remaining player from the Blue Jackets inaugural season. During an injury-shortened 2008–09 season in which Klesla appeared in only 34 games, he scored a goal and nine points, helping Columbus to their first ever post-season appearance. In four playoff games, Klesla had an assist as the Detroit Red Wings swept the Blue Jackets. Injury problems plagued Klesla in the 2009–10 season, as he played in only 26 games, scoring two goals and eight points. In 2010–11, Klesla had three goals and 10 points in 45 games with Columbus. On February 28, 2011, the Blue Jackets traded Klesla and Dane Byers to the Phoenix Coyotes for Scottie Upshall and Sami Lepistö. Klesla was the last Blue Jacket from the team's first season still active on the team before he was traded in 2011. Klesla went on to play 16 regular season and four playoff games for the Coyotes in 2011, registering one goal. Klesla suffered an injury in a September 15, 2013, pre-season game against the Los Angeles Kings and was taken off the ice on a stretcher. The hit was delivered by Kings' forward Jordan Nolan, who received four minutes in penalties and a 10-minute misconduct for the hit. On November 26, 2013, Klesla was placed on waivers by the Coyotes and the following day, he was sent down to play with the Coyotes’ American Hockey League affiliate, the Portland Pirates. On December 19, 2013, Klesla was recalled to the Coyotes. Klesla featured in 25 games with the Coyotes, primarily as an extra defenseman, before on March 4, 2014, he was traded to the Washington Capitals in a deal along with Chris Brown, and a fourth-round pick in the 2015 NHL Entry Draft for Martin Erat and John Mitchell. On March 5, 2014, just one day after being traded to the Capitals, Klesla was traded to the Buffalo Sabres, along with Michal Neuvirth, for Jaroslav Halák and a third-round draft pick. On March 8, Klesla decided to not report to the Sabres, stating, "ith all due respect to the Sabres organization, I decided this week not to continue playing hockey this season. It has been a tough year for injury and moving several times to new teams...I will now take some time off and get ready to continue my career in Europe. I would like to thank my fans and all the people that have helped me. I am grateful for the career I have had in the NHL and all the people that I have met along the way who have supported me and my family." The Sabres suspended Klesla for not reporting to their AHL affiliate, the Rochester Americans. Klesla officially ended his NHL career when he returned to his native Czech Republic, signing for a second stint with HC Oceláři Třinec on a two-year contract on June 25, 2014.
