Upon entering Thelma Yellin, Israel's leading high school for the arts, Avital switched to acoustic bass and began studying and arranging jazz.

[2] He spent a year in the Israeli Army Orchestra and then moved to New York in 1992 where he began playing, recording, and touring professionally.

[4] In 1995 and 1996, Avital made an impact on the New York jazz scene with a series of breakout piano-less groups at the original Smalls Jazz Club, including a classic sextet with four saxophones, bass and drums, alternately included saxophonists Myron Walden, Mark Turner, Gregory Tardy, Joel Frahm, Charles Owens, Grant Stewart, Jay Collins and Jimmy Greene, and drummers Ali Jackson, Joe Strasser and Daniel Freedman.

In 2001, Avital released his debut album, Think With Your Heart, featuring Gregory Tardy, Jay Collins, Myron Walden, Joel Frahm, Jimmy Greene, Joshua Levitt, Daniel Freedman and Marlon Browden.

In 2005, Avital returned to New York and released three albums, including two from the Smalls recording archives and a fourth with the group Third World Love.

Avital's album Abutbul Music was released worldwide in March 2016 on the Paris-based Jazz Village label by Harmonia Mundi.