The party was formed in December 2018, when Naftali Bennett, Ayelet Shaked, and Shuli Mualem left the Jewish Home, using the registration of the unused Tzalash party. The party's legal name remains Tzalash, though it was restyled as an abbreviation for Tzion LeShevah, rather than the previous Tziyonut Liberaliyut Shivyon of the original Tzalash. Among the reasons given for the split was the purely religious nature of the Jewish Home. It was announced on 2 January 2019 that Caroline Glick, a columnist at The Jerusalem Post, had joined the party. Deaf rights activistShirley Pinto joined the party on 8 January 2019; Shaked stated that Pinto would be an "effective advocate for the rights of people with disabilities". In the September 2019 election, it joined the Yamina alliance, alongside the Jewish Home and Tkuma. The alliance officially split into two factions on 10 October. The New Right also unsuccessfully attempted to negotiate an alliance with Zehut. On 8 November 2019, Prime Minister Benjamin Netanyahu announced that the New Right would be merging with his ruling Likud party, though Shaked rebutted the idea the next day. Prior to the 2020 Israeli legislative election, the New Right entered talks with the New Liberal Party for an electoral alliance. Bennett subsequently approached Zehut leader Moshe Feiglin for an alliance, though Feiglin declined the offer. On 14 January 2020, the New Right announced it had formed an electoral alliance with Tkuma. The party reformed the Yamina alliance on 15 January, with The Jewish Home and Tkuma again joining. Bennett rejected the prospect of expanding the alliance to include Otzma Yehudit, despite pressure from Netanyahu. On 22 April 2020, it was reported that Bennett was now "considering all options" for Yamina's political future, including departing from Netanyahu's government, which had just agreed to form a joint government with leader of the oppositionBlue and White party Benny Gantz, and joining the opposition. Bennett was said to be unhappy with the new coalition government's decision to hold back on the issue of judicial reform. On 14 May 2020, The Jewish Home's only Knesset member Rafi Peretz ended his status as a member of Yamina, and agreed to join Netanyahu's new government as well. On 15 May, the New Right, along with Tkuma, split with Netanyahu and made the Yamina alliance a member of the opposition. On 17 May 2020, Bennett met with Gantz, who also succeeded him as Defence Minister, and declared that both Yamina parties were now "head held high" members of the opposition.
The New Right platform, as detailed by its website, is:
Promotion of cooperation between religious and secular Jews.