A Jew who has entered the Catholic Church. Hebrew is his ethnicity, his membership in God’s people Israel. Catholic is his faith, his membership in the Church of the new Israel. Many Jews who become Catholic call themselves Hebrew Catholics because Hebrew is historically associated with Abram the Hebrew, who received the eternal election in the everlasting covenant with God, and whom Melchizedek blessed with bread and wine foreshadowing Rabbi Yeshua.
Also, sometimes, “Catholic Jew” or “Catholic of Jewish origin.”