One month later, Martincová once again came through qualifying at the Baku Cup, defeating Oksana Kalashnikova in the first round,[3] but losing to Tadeja Majerič in the second.

[4] In 2014, first WTA Tour event for Martincová was the Nürnberger Versicherungscup where she qualified for the main draw, and then lost to Anastasia Rodionova.

[6] At the Coupe Banque Nationale in Quebec City, Martincová once again passed qualifying, but again lost in the first main-draw round, this time to Shelby Rogers.

[7] In 2015, Martincová made her first WTA Tour quarterfinal at the Brasil Tennis Cup after victories over Quirine Lemoine and Ajla Tomljanović.

In 2016, she improved her best performance on WTA Tour, making it to the semifinals of the Tournois de Québec, and earning victories over Barbora Krejčíková, Ekaterina Alexandrova and Jessica Pegula.

Martincová realized her best performance at a major championship in 2017, reaching the first round at the US Open by defeating Valentini Grammatikopoulou, Vera Lapko and Georgia Brescia in qualifying.

She achieved her best performance at Wimbledon, reaching the first round by defeating Xu Shilin, Caroline Dolehide and Anna Blinkova in qualifying.

Martincová started her grass-court season with quarterfinal showings in Nottingham and Birmingham, scoring big wins over former top-10 members and major champions, Samantha Stosur and Jeļena Ostapenko.

Entering Wimbledon in good form, she stormed into the third round on grandslam for the first time, defeating former quarterfinalist Alison Riske and Nadia Podoroska.

In September 2021, she reached her first WTA 500 level quarterfinal in 2021 Ostrava Open, defeating Kateřina Siniaková and Anastasia Pavlyuchenkova before losing to eventual finalist Maria Sakkari.

Partnering Marta Kostyuk, Martincová won the doubles title at the 2022 Zavarovalnica Sava Portorož, defeating Tereza Mihalíková and Cristina Bucșa in the final.

She then recorded her first year tour-level win at the Miami Open where she defeated Tamara Korpatsch, before losing to Beatriz Haddad Maia.