Noah Webster's Dictionary (n.) The office, dignity, or position of a high priest.

Multi-Version Concordance High-priesthood (2 Occurrences) Mark 2:26 how he entered the house of God in the High-priesthood of Abiathar, and ate the Presented Loaves--which none but the priests are allowed to eat--and gave some to his men also?" (WEY) Luke 3:2 during the High-priesthood of Annas and Caiaphas, a message from God came to John, the son of Zechariah, in the Desert. (WEY RSV)