He studied law at the Hebrew University of Jerusalem and served as an Officer of Justice in the Israel Defense Forces during his national service.

Following Likud's victory in the 1977 election, Nissim was appointed Minister without Portfolio in Menachem Begin's government in January 1978.

In 2017, Prime Minister Benjamin Netanyahu appointed Nissim to lead an overhaul of the conversion system in Israel.

Nissim proposed removing control of it from ultra-Orthodox-dominated Rabbinate, creating a new state-run Orthodox authority instead.

Ultimately, the idea was rejected "due to ultra-Orthodox and national religious opposition.