[5] He played his first match at a Grand Slam at the 2016 Australian Open, where he lost to fellow qualifier Marco Trungelliti in the first round.

[6] At the 2016 BNP Paribas Open Kovalík won his first match at ATP level, defeating another qualifier Pierre-Hugues Herbert in the first round.

[citation needed] Kovalík won the 2016 Capri Watch Cup, his second title on the ATP Challenger Tour.

[12] Kovalík reached another ATP level semifinal at 2018 German Open in Hamburg, where he lost to the defending champion Leonardo Mayer.

[16] Following a third final showing for the season at the 2024 Upper Austria Open in Mauthausen, where he lost to Lucas Pouille, Kovalik returned in the top 150 in the rankings on 20 May 2024.