In 1898, at age 12, he was invited to be part of the founding core of the Etz Chaim yeshiva in Maletz under the leadership of Rabbi Zalman Sender Kahana Shapira.

He briefly studied at the Mir Yeshiva but returned to Maletz, where he became a prominent student of Rabbi Shimon Shkop.

He established an umbrella organization for all the Jewish communities in the area, brought in students from Europe to strengthen the local yeshiva, and founded the Liverpool Academy for Torah Studies.

During World War II, Rabbi Unterman worked on behalf of Jewish refugees from Germany who were treated as enemy subjects by England.

For example: There is room to be lenient in this difficult situation when it is impossible to prevent foreign immigrants from mixing among the children of Israel... One must act with these individuals needing conversion according to the law of the Torah, with sensitivity and understanding, taking into account the spiritual hardship these brothers of ours have endured.

[8] He also wrote in response to Rabbi Ketheriel Fishel Tikhuresh's article about the question posed by Bar-Ilan University on using embryonic stem cells:[9] I received your letter with a broad and detailed halachic discussion on the question of whether it is permissible to use tissue extracted by biopsy from stillborn fetuses, which never had independent life, for the purpose of treating children; from your words, I see that you consulted prominent rabbis who agreed to permit.

Therefore, after examining the matter, I too agree to permit (emphasis in the original) conducting research using this material for the purpose of healing patients.Rabbi Unterman supported the recitation of Hallel on Yom Ha'atzmaut, but since we do not have the authority that the sages had to establish new blessings, he hesitated about whether to recite the blessing before Hallel, invoking the name of God.

On the other hand, on Jerusalem Day, Rabbi Unterman argued that Hallel should be recited with a blessing, as it is a celebration of a transition from death to life.