During the 1960s, Turnovský was appointed chief conductor of the Radio Symphony Orchestra Plzeň (1963-66), the Sächsische Staatskapelle Dresden and Semperoper (1966-1968), the Norwegian State Opera (1975-80), the Opera in Bonn (1979-83), and the Prague Symphony Orchestra (1992-96). He was also permanent guest conductor of the Czech Philharmonic Orchestra (1960-1968).
After the entry of the Warsaw Pact nations into Czechoslovakia (Prague Spring), Turnovský immigrated to Austria and was granted Austrian citizenship. However, following the revolutions of 1989 he returned to central and Eastern European countries.
After Turnovský gained Austrian citizenship, he conducted many more symphony orchestras, including the New York Philharmonic, the Cleveland Orchestra, the Detroit Symphony Orchestra, the London Symphony Orchestra, the Bavarian Radio Symphony Orchestra, l'Orchestre de la Suisse Romande, the Vienna Symphony, the Bamberg Symphony, the Toronto Symphony Orchestra, the City of Birmingham Symphony Orchestra, the Royal Liverpool Philharmonic, the Tokyo Metropolitan Symphony Orchestra, and other orchestras.