He started his musical career as principal trumpet of the Radio Symphony Orchestra of the Netherlands when he was 21 while studying at the Maastricht Conservatory. After 9 years, he was appointed as principal trumpet of the Royal Concertgebouw Orchestra Amsterdam, holding this position from 1991 until 2010. In addition, he taught the trumpet at the Conservatorium van Amsterdam from 1993 until 2010.

As a chamber musician, Frits Damrow played in different groups such as the Amsterdam Bach Soloists, the Netherlands Wind Ensemble, the Ebony Band, the Brass Quintet and Brass Ensemble of the Royal Concertgebouw Orchestra.

Since 2009, he has been Professor of trumpet at the University of the Arts in Zürich, Switzerland (Zürcher Hochschule der Künste).

He is a regular teacher and soloist at many summer courses and festivals, like the Hamamatsu Summer Wind Academy and the Affinis Festival in Japan, Musica Verano in Mexico, Ionian Summer Academy in Greece, Curso International de Musica in Spain, Blekinge International Brass Academy and the Aurora Festival in Sweden, the Tbilisi Wind Festival in Georgia and Sauerland Herbst in Germany.

He taught master classes at numerous institutes: North Western University in Chicago, San Francisco Conservatory, Curtis Institute in Philadelphia, Royal Conservatory in Brussels, at the Music Academies in Freiburg, Munich, Cologne and Stuttgart, at the Tchaikovsky Conservatory and Gnesin Academy in Moscow, State Conservatory in Athens, Shobi University in Tokyo, National University in Seoul and several universities in China.