In 1958 he made his operatic debut with the New Orleans Opera Association, in the secondary role of Pong in the local premiere of Turandot, conducted by Renato Cellini.
In the next few seasons, he would become acclaimed as one of the world's leading Heldentenors, appearing at Brussels (Les contes d'Hoffmann staged by Maurice Béjart, 1961), Wuppertal (as Mephisto in Busoni's Doktor Faust and in Peter Grimes, 1962), Lisbon (the Kaiser in Die Frau ohne Schatten, 1962; and Herodes in Salome, 1975), Kassel (Die Frau ohne Schatten and Siegfried, 1962; and Tannhäuser conducted by Christoph von Dohnányi, 1964), Amsterdam (Doktor Faust, 1962; and as Prince Chouïsky in Boris Godunov, 1989), and Vienna (Ariadne auf Naxos, 1965; Der fliegende Holländer, 1967; and Einem's Der Besuch der alten Dame, 1973).
In the summer of 1963, he made his debut at the Bayreuth Festival as Kunz Vogelgesang in Wieland Wagner's production of Die Meistersinger, with Anja Silja as Eva.
In his native Copenhagen, Parly sang in Fidelio (as Florestan, 1963), Der fliegende Holländer (as Erik, 1963), Tannhäuser (1964), Elektra (as Ägisth, 1966) and Boris Godunov (directed by Harry Kupfer, 1988).
In the summer of 1968 he made his debut at Bayerische Staatsoper in Tristan und Isolde, but the conductor, Joseph Keilberth, died conducting the second act and the performance was cancelled.
[2] In 1967, Parly made his debut at the Teatro alla Scala in Salome, followed by Tannhäuser (1967), and returned in 1971 for the Tambourmajor in Berg's masterpiece, Wozzeck, conducted by Claudio Abbado.
In 1981 he sang Loge at the Cincinnati Opera, and the following year was found singing Herodes in Salome there, with Marisa Galvany in her first assumption of the title role.