Only Jewish high priests could have had influence in the Sanhedrin, which served as the Supreme Court and legislative council of Ancient Israel.

According to the 1917 Catholic Encyclopedia, “The high-priest alone might enter the Holy of Holies on the day of atonement, and even he but once a year, to sprinkle the blood of the sin-offering and offer incense: he prayed and sacrificed for himself as well as for the people (Leviticus 16).”  Aaron was the first high priest.

“The typical character of the high-priest is explained by St. Paul (Hebrews 9), where the Apostle shows that while the high-priest entered the "Holy of Holies" once a year with the blood of victims, Christ, the great high-priest, offered up His own blood and entered into Heaven itself, where He "also maketh intercession for us" (Romans 8:34; see Piconio, "Trip. Expos. in Heb.", 9).

“The consecration of Aaron consisted in washings, investment with costly vestments, anointing with holy oil, and the offerings of various sacrifices (Exodus 29). As a sign that Aaron was endowed with the fullness of the priesthood, Moses poured over his head the oil of anointing (Leviticus 8:12), while the other Aaronites, as simple priests, had only their hands anointed (Exodus 29:7, 29). The high-priest was for the Jews the highest embodiment of theocracy, the monarch of the whole priesthood, the special mediator between God and the People of the Covenant, and the spiritual head of the synagogue. (Source: Catholic Encyclopedia)