Sharir was born in 1932 in Tel Aviv, where he attended high school. He studied law at the Hebrew University of Jerusalem and was certified as a lawyer. From 1954 to 1964 he was secretary of the General Zionist faction in the Knesset. He was the director of the economics department of the Jewish Agency in the United States from 1964 to 1967 and director of the coordinating bureau of the economic organizations of the employers in Israel from 1967 to 1970. He was the economic consul in Atlanta from 1970 to 1972 and then in Western United States until 1974. From 1974 to 1977 he was General Secretary of the Liberal Party and its chairman of the national board.
He was elected to the ninth Knesset in 1977 for the Likud and again in 1981, 1984 and 1988. He was a member of the finance committee in the ninth Knesset and of the foreign affairs & defense committee in the twelfth. He was the Minister of Tourism in the tenth Knesset and also Minister of Justice in the eleventh.