He attended New York University and graduated with honors from the University of Iowa.
He began acting, directing and teaching in Cleveland, Ohio. A veteran of the "Golden Age" of live television (he played Quasimodo in a live Robert Montgomery Presents (1950) version of "The Hunchback of Notre Dame"), for the same show played the lead in "A Case of Identity", later turned into the film The Wrong Manitoba, he was the first actor to play Albert Einstein on television Ellenstein made his first film in 1954 (Metro-Goldwyn-Mayer"s Rogue Cop), he was featured in Alfred Hitchcock"s North by Northwest.
In 1961, he played the mobster Legs Diamond in an episode of National Broadcasting Company"s 1920s crime drama The Lawless Years with James Gregory.
Among his television appearances, Ellenstein guest starred in three episodes of Perry Mason. In 1957 he played defendant John Addison in "The Case of the Vagabond Vixen." In 1959 he played murder victim Arthur Cartright in "The Case of the Howling Dog," and in 1960 he played Medical Examiner Doctor McBride in "The Case of the Madcap Modiste." He also made three guest appearances on The Untouchables, five appearances on The Wild Wild West, four on Ironside, and five on Mission: Impossible.
He also directed television with an episode of the 1960s sitcom, Love on a Rooftop with Judy Carne and many live television episodes. Ellenstein had over 200 television appearances.
He performed hundreds of stage roles as an actor.
He directed many theatre productions in New York, Los Angeles and in regional theater. He was artistic director of The Company of Angels and Founding Artistic Director of the Los Angeles Repertory Company. He is best known for having played the villain in the pilot episode of Moonlighting (1985), and then the Federation President in Star Trek IV: The Voyage Home (1986).
Ellenstein taught theatre professionally and academically for over 50 years, founding the Academy of Stage and Cinema Arts in Los Los Angeles
He died in Los Angeles, California of natural causes on October 28, 2010 at age 87.