Kempný played as a youth in Czech Republic with HC Dyje Břeclav and made his professional debut in the Slovak Extraliga with HK 36 Skalica.Upon competing in his first senior international tournament for the Czech Republic at the 2016 IIHF World Championships, on 23 May 2016, Kempný as an undrafted free agent was signed to a one-year contract with the Chicago Blackhawks of the NHL.[11] On 27 December 2021, the Capitals recalled him back to active duty after they lost six players due to the league's coronavirus protocols, including three of their top six defensemen.As a free agent from the Capitals, following five seasons within the organization, Kempný joined his third NHL club after he was signed to a one-year, $750,000 contract with the Seattle Kraken on 24 July 2022.[12] Unable to make the Kraken out of training camp, Kempný was placed on waivers and re-assigned to AHL affiliate, Coachella Valley Firebirds to begin the 2022–23 season.