The Washington Capitals wanted more depth on defense as they prepared for the Stanley Cup Playoffs in 2018. That's why the Capitals acquired Kempny in a trade with the Chicago Blackhawks on Feb. 19, 2018, two days after getting an up-close look at the 27-year-old native of the Czech Republic in a 7-1 loss.

Kempny signed with the Blackhawks on May 23, 2016, after a breakout season in the Kontinental Hockey League and his first appearance for the Czech Republic at the 2016 IIHF World Championship. He played 50 games for the Blackhawks in his first NHL season, finishing with eight points (two goals, six assists). That was enough to convince Chicago to keep the pending restricted free agent, signing him to a one-year contract on May 27, 2017.

But Kempny's playing time in Chicago declined in 2017-18, and he had seven points (one goal, six assists) before being traded to the Capitals. He settled in as the stay-at-home partner of high-scoring John Carlson and scored his first Stanley Cup Playoff goal in Game 1 of the Eastern Conference Final against the Tampa Bay Lightning. Kempny finished with five points (two goals, three assists) in 24 games during Washington's run to the first Stanley Cup championship since entering the NHL in 1974.

Kempny settled into a regular role with the Capitals in 2018-19 and finished with NHL career highs in goals (six), assists (19), points (25) and plus-minus rating (plus-24). He was hampered by injuries during the 2019-20 season but still finished with three goals, 18 points and a plus-19-rating.

Kempny signed a one-year, $750,000 contract with the Seattle Kraken on July 25, 2022.