He studied with Leonard Bernstein, becoming one of his assistant conductors at the New York Philharmonic. He also studied with Serge Koussevitzky at Tanglewood, and at the Juilliard School. He was Assistant Conductor with the San Francisco Symphony. He led the New York Philharmonic on tours to Canada and Japan in 1960-61. He was guest conductor with the University of the Pacific in 1961. He became Associate Conductor with the Boston Symphony Orchestra from 1962 to 1967.
He was appointed Chief Conductor of the Malmö Symphony Orchestra in Sweden 1969-1974.
From 1975 to 1979 was the Chief Conductor of the Adelaide Symphony Orchestra in Australia. He has also been associated with Arnhem Philharmonic Orchestra in Netherlands.
Elyakum Shapirra was the first conductor of Alexander Scriabin's Prometheus "The Poem of Fire" in England in 4 May 1972 at the Royal Albert Hall with the London Symphony Orchestra. Also conducted the Royal Philharmonic Orchestra and soloist Georges Pludermacher in the posthumous world premiere of Jani Christou's Toccata for Piano and Orchestra (1962), on 23 April 1973 in Oxford.
In 1972 Shapirra made the first commercial recording of Anton Bruckner's Symphony in F minor (Study Symphony), with the London Symphony Orchestra. He has also recorded Bruckner's Overture in G minor with the LSO. Other symphonic recordings include Leonard Bernstein's 1st and 2nd symphonies. He has also recorded other standard orchestral repertoire with various orchestras, as well as Israeli, Yemeni and Yiddish songs with popular singers.