In 1931, he premiered a composition and appeared in concert as a pianist at the Prague Mozarteum. His conducting debut was made in 1934 with a production of La traviata at the German Opera, where he had been serving as an assistant to Szell. He composed his Four Songs for Voice and String Quartet in 1935 and continued his piano activity with the Czech Trio from 1933 until the German occupation in 1938. The trio then escaped to London and remained together until 1942. Süsskind re-activated his conducting as music director of the Carl Rosa Opera Company (1943 - 1945) and made his orchestral debut conducting the Liverpool Philharmonic Orchestra (1945). After becoming a British citizen in 1946, he went to Glasgow to serve as music director for the Scottish Orchestra (later the Scottish National Orchestra). In 1953, Süsskind moved to Australia to direct the Victoria Symphony Orchestra in Melbourne until 1955. During that period, he made tours of America and the Far East. Then, moving again, he directed the Toronto Symphony Orchestra from 1956 to 1965, giving the Canadian premieres of Bruckner and Mahler symphonies, and founded the National Youth Orchestra of Canada in 1958. Meanwhile, he was music director for the Aspen Music Festival in Colorado (1962 - 1968) and later, the St. Louis Symphony Orchestra (1968 - 1975), which Süsskind built into a major institution, and the Mississippi River Festival in Edwardsville, IL (1969 - 1975). From 1968 through 1975, Süsskind taught at the University of Southern Illinois. His conducting students included Leonard Slatkin and Gerhardt Zimmermann. His compositions at this time included Nine Slovak Sketches for Orchestra and a Passacaglia for Timpani and Chamber Orchestra (1977).
As guest conductor, Süsskind led major orchestras in Europe, the U.K., and North America. He was the music advisor and principal guest conductor of the Cincinnati Orchestra from 1978 until his passing in 1980.
Süsskind's discography contains more than 55 albums and performances with some of the most noted performers of the twentieth century: Jascha Heifetz, Arthur Rubenstein, Glenn Gould, Dennis Brain, Pierre Fournier, Joan Hammond, Elisabeth Schwarzkopf, Kirsten Flagstad, Lili Krauss, Szymon Goldberg, Yehudi Menuhin, Artur Schnabel, Leonard Pennario, Shura Cherkassky, Neveu, Tito Gobbi, Victoria de Los Angeles, and many others.