He completed two years in a circus school, traveled throughout Europe performing on the streets as a clown, and ended up working in the Parisian Cirque Pawelles.

Following his studies with Nativ, Ivanir joined the Gesher Theater, a Tel Aviv-based company composed of emigrants from the former USSR.

Ivanir's first major film role was in Steven Spielberg's 1993 Oscar-winning epic Schindler's List, where he played Marcel Goldberg.

His biggest part to date was on the critically acclaimed A Late Quartet, released from RKO pictures in the United States, in fall 2012.

As of August 2019, Amazon Prime is airing worldwide the Israeli hit show "The Beauty and the Baker", with Ivanir playing the part of Zvika Granot.

In 2018, he co-starred in the film Entebbe, directed by José Padilha, the creator of Narcos, and Bill Hader's HBO comedy Barry, in which he recurs as three Chechen brothers.

He appeared in The Red Sea Diving Resort, as the head of the Mossad, alongside Sir Ben Kingsley, Chris Evans and Greg Kinnear.