Hacham Avraham David Shalem was born to Esther and Hacham David Shalem in Jerusalem on 26 Tevet, 5688 (1928). As a child, Hacham Avraham David Shalem studied at the Mizrahi Talmud Torah. He continued his studies at the Sha'arei Zion yeshiva, founded by Rishon LeZion Hacham Ben Zion Meir Chai Uziel in Jerusalem's Nahalat Shiva neighborhood.
Hacham Avraham David Shalem was ordained to the rabbinate and conferred as dayan by Rishon LeZion Hacham Ben Zion Meir Chai Uziel, as ritual slaughterer and bodek by Hacham Mordecai Meyuhas, Head of the Jerusalem Sephardi community rabbinic court (Av Beit Din) and as mohel by Hacham Yaakov Sasson.
He joined the Haganah during Israel's War of Independence in 1948. In 1949, Hacham Avraham David Shalem married his cousin Sarah, and they had a son and a daughter. His wife died within three years of their marriage.
In 1950, Hacham Avraham David Shalem complied with Rishon LeZion Hacham Ben Zion Meir Chai Uziel's request and relocated to Lima, capitol of Peru, to lead its Jewish community.
Hacham Avraham David Shalem taught and educated to a love of Torah, the Jewish nation and the Land of Israel. He helped organize Jewish life in Lima and took an active part in the United Jewish Appeal. After several years, he moved to Seattle, USA, and served as Rabbi of the Ezra Bessarot synagogue; he later moved to Mexico City, where he served as Rabbi of the Har Sinai congregation.
Hacham Avraham David Shalem returned to Israel in 1977 to head the Or HaMizrach Institute for the publication of ancient manuscripts, the Sephardi Orphanage, and the seminary for avreichim that was established on the facility. During this period, Hacham Avraham David Shalem was also active in the Va'ad Ha'Eda HaSepharadit, and in the Committee for the Publication of Rabbi Uziel's Writings. Hacham Avraham David Shalem maintained his contact with the Jewish communities of Latin America and translated numerous books on Halacha to Spanish.
Hacham Avraham David Shalem passed away on 23 Elul 5774 (2014). His books include Eshed HaNehalim, in three parts – a commentary on the Book of Ecclesiastes, Na'ot Desheh – a prayer book for Rosh Hashanah and Yom Kippur according to the Sephardi custom, and a Spanish translation and commentary of the Psalms.