Zohar was born and raised in Kiryat Gat. His father Eli was an immigrant from Morocco and his mother Dina was from Tunisia. Zohar served in the Israel Defense Forces and reached the rank of Sergeant. He then studied law, gaining an LLB from the College of Law and Business and an MA from Bar-Ilan University, and worked in real estate. He became chairman of Maccabi Kiryat Gat basketball club in 2004, serving until 2014. In 2005 he was elected to Kiryat Gat City Council. He was elected head of the city's Likud list in 2013, and became Deputy Mayor.
Zohar is married to Yamit, who also works in real estate, and has four children.
Zohar is an advocate for observing Shabbat. He filed a bill that would outlaw forcing business owners to work on Saturdays. In addition, business owners would be able to file a claim for damages against members who violate Shabbat that harm them financially. Zohar stated in a radio interview for an ultra-Orthodox Jewish station that "Anyone who doesn't believe in God is delusional".
Zohar supported the creation of a new Israeli national holiday, Yom HaAliyah (Hebrew: יום העלייה, Aliyah Day) to be celebrated annually on the tenth of the Hebrew month of Nisan (Hebrew: י’ ניסן). On 21 June 2016, the Knesset voted in favor of adding Yom HaAliyah to the national calendar. The Yom HaAliyah bill was co-sponsored by Knesset members from different parties in a rare instance of cooperation across the political spectrum. The day chosen for Yom HaAliyah is, according to the biblical narrative, the day Joshua and the Israelites crossed the Jordan River at Gilgal into the Promised Land. It was thus the first documented "mass Aliyah".