Eli Eban was appointed principal clarinetist of the Jerusalem Symphony Orchestra under Lukas Foss immediately after graduating from the Curtis Institute of Music and shortly thereafter he joined the Israel Philharmonic Orchestra at the invitation of Zubin Mehta. During thirteen seasons with the Israel Philharmonic, he performed and recorded all the major orchestral repertoire with the world's finest conductors, including Claudio Abbado, Leonard Bernstein, Christoph von Dohnanyi, Charles Dutoit, Christoph Eschenbach, James Levine, Kurt Masur, Simon Rattle, Leonard Slatkin, Georg Solti, and Klaus Tennstedt.

Mr. Eban was featured as soloist with the Israel Philharmonic Orchestra on many occasions and he has also performed concertos with the English Chamber Orchestra, the City of London Sinfonia, the Salzburg Camerata Academica, the Chamber Orchestra of Philadelphia, the Israel Camerata Jerusalem and the Louisville Orchestra, among others. He tours extensively as a chamber musician, collaborating with renowned artists and ensembles. He has been guest artist with the Alexander, Audubon, Orion, St. Petersburg, Tel Aviv and Ying quartets and was a frequent participant of the famed Marlboro Music Festival in Vermont. While at Marlboro, he was invited by legendary violinist Sandor Vegh to perform at the inaugural season of the Prussia Cove festival in England, where he drew critical acclaim from the London Guardian for his "high-powered, electrifying performances". His subsequent recordings for Meridian Records, London, were cited by the Penguin Guide to CDs as being"full of life and highly sensitive". He has also recorded for the Saphir, Crystal and Naxos labels. He was a member of "Myriad" (a chamber ensemble formed by members of the Cleveland Orchestra) and has often traveled to Eastern Europe to perform and teach at the invitation of the European Mozart Foundation.

In high demand as teacher, Eli Eban was a visiting professor at the Eastman School of Music for two years before joining the faculty of the Jacobs School of Music at Indiana University