From hieros ('sacred/holy'). Hierosune refers to the priestly office or function โ the role and dignity of the priest as mediator between God and humanity. Used in Hebrews to contrast the Levitical priesthood with Christ's eternal priesthood.
Hebrews 7 builds the theological case for Christ's superior priesthood using hierosune. The Levitical hierosune was impermanent, transferable (because priests died), and ultimately ineffective โ it could not bring the worshipper to perfection. Christ's hierosune, established by God's oath ('Thou art a priest forever after the order of Melchizedek'), is permanent, untransferable, and perfectly effective. The 'better hope' (7:19) gives us actual access to God โ not the shadow-access of animal blood but the real access of Christ's own blood. Believers share in this priesthood (1 Peter 2:9) โ a royal, holy hierosune.