She reached the French Open quarterfinals with her compatriot Klaudia Boczová, losing to the eventual champions and third seeds, Ksenia Milevskaya and Urszula Radwańska.

With her compatriot Lenka Juríková, she reached the Wimbledon quarterfinals and lost to the eventual runners-up Misaki Doi and Kurumi Nara.

[1] After defeating Stefanie Vögele and Hsieh Su-wei, Kučová reached the quarterfinals in Kuala Lumpur, where she lost to the second seed Elina Svitolina despite winning the first set 6–1.

Kučová won her first WTA 125 title at the Sparta Prague Open, defeating Elisabetta Cocciaretto in the final.

1 and defending champion, Ashleigh Barty, in the second round, losing the match in three sets[3] In July 2021, she reached her first WTA 250 final, at the Poland Open, but lost to Maryna Zanevska.

[4] At the 2021 US Open, Kučová qualified for the first time in five years, after entering the main draw as lucky loser, and won her first match at this major against Ann Li.

[6] In January 2023, she entered the Australian Open using protected ranking, losing in the first round to qualifier Diana Shnaider in straight sets.

[7] Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.