In the liturgical services, the bishop is referred to as ὁ ἀρχιερεύς, which is indeed the Greek word that many translate as "high priest" in the NT. This is true in rubrics, commemorations, and in hymns about famous, saintly bishops, e.g. St Nicholas. They are also called "archpastors" in the same sources and others.
Actually, you have all just called them high priest. The word "heirarch" is an Anglization (and distortion) of the Greek ἀρχιερεύς. "heir-" coming from the word ιερεύς (iereus) meaning "priest" and "-arch" coming from the word "ἀρχῇ" (arche) meaning "first, leading."
I love Greek!