Katarína Veselská was born in Trnava, Slovakia, in 1989. She began her musical training at the Trnava Music School and continued her studies at the Bratislava Conservatory, later completing her education at the University of Music and Performing Arts Graz under Prof. Eszter Haffner. She has participated in numerous masterclasses, including 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.

Since 2014, she has held the position of second violinist in the Varga Quartet Vienna.

Alongside her work with the quartet, she regularly performs chamber music with renowned artists such as Gottfried 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. Her performances have taken her to prestigious venues including the Vienna Musikverein, the Vienna Konzerthaus, Suntory Hall in Tokyo, the Slovak Philharmonic, and the Gasteig in Munich.

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.