Zsombor, an early keyboard specialist and conductor, is one of the leading figures of the young musician generation in Hungary. He studied harpsichord and the organ at the Ferenc Liszt Academy of Music in Budapest with Miklós Spányi, where he graduated with the highest honours, and where he is a guest teacher now. He continued his studies at the Conservatorium van and was taught by Menno van Delft (harpsichord, clavichord) and Richard Egarr (harpsichord, Amsterdam fortepiano), and on the organ by Jacques van Oortmerssen. He also holds a degree in medicine from Semmelweis University, Budapest.

He has given recitals in many European countries and in the United States of America as a soloist, conductor and as continuo in various orchestras. Zsombor is the founder and artistic director of Hungarian baroque orchestra Harmonia Caelestis (founded in 2015) in Budapest, and he is a passionate piano four-hands player with his partner and twin brother, Gergely under the name Piano e Forte Duo. Zsombor has recorded seven solo recordings for different labels.