Katarína Veselská was born in Trnava, Slovakia, in 1989. She began developing her musical talent at the Trnava Music School. She later studied at the Bratislava Conservatory and the University of Music and Performing Arts Graz with Prof. Eszter Haffner. She has also participated in several masterclasses: the Neuberger Kulturtage (with Eszter Haffner, Veronika Schulz, and Günter Teuffel), the Hamburg Summer Music Academy (Thomas Brandis), the Humilitas Masterclass (Giaccomo Tessini and Simone Jandl), and the Summer Campus of the Royal Danish Academy of Music (Sergei Azizian). She also studied chamber music with Prof. Herbert Kefer and Prof. Rudolf Leopold.

She has held the position of second violin in the Varga Quartet Vienna since 2014.

She also regularly performs in chamber music with various renowned artists such as Gottfired Boischits (Vienna Philharmonic), Dalibor Karvay (First Concertmaster of the Vienna Symphony Orchestra), Mario Hossen, Lilliana Kehayova, Eszter Haffner, Othmar Müller, Ivica Encingerová-Gábrišová, Vladislava Luchenko, and the Quasars Ensemble. Performances have taken place at venues including the Vienna Musikverein, Vienna Konzerthaus, Suntory Hall Tokyo, the Slovak Philharmonic, and the Gasteig in Munich.