He serves as the ga'avad[1] (Gaon Av Beis Din) of the Edah HaChareidis in Jerusalem, and the rabbi of the Gra Synagogue in the Har Nof neighbourhood.

His parents hosted numerous rabbis who came to London to raise money for their yeshivas, among them Elchonon Wasserman, who after learning with Sternbuch declared that he was a davar sheyeish bo mamash (a boy of substance).

They moved to a small nearby village where he shared a room with Eliyahu Eliezer Dessler, author of Michtav me-Eliyahu, who predicted that Sternbuch would someday be one of the gedolei hador (greatest of the generation).

[6] Due to the increasing threat of a Nazi invasion of Britain, Sternbuch's mother attempted to arrange his safe passage to Canada or the United States.

[8] Sternbuch resides in the Har Nof neighbourhood of Jerusalem, where he is the rabbi of the local Gra Synagogue, named after the Vilna Gaon of whom he is a direct descendant.

[9] He enrolled in the Hebron Yeshiva, and cultivated relationships with rabbis Soloveitchik, the Chazon Ish and Dov Berish Weidenfeld, with whom he used to meet regularly in their homes.

Yechezkel Abramsky encouraged Sternbuch to devote himself to strengthening Torah study in Rosh HaAyin, a nearby town with a substantial Yemenite Jewish immigrant population.

[13][14] On July 20, 2023, Elyakim Schlesinger appointed Sternbuch as ga'avad (Gaon Av Beis Din) of the Edah HaChareidis, succeeding Yitzchok Tuvia Weiss, who died in 2022.

[15] In September 2018, Sternbuch criticized British Chief Rabbi Ephraim Mirvis for publishing an educational pamphlet warning against LGBT bullying in Orthodox schools.