2 orders of priesthood divide here. The temporary kind, made without an oath, is the mind's ordinary religious effort that rises and falls and passes with the body. The eternal kind, sworn and unchanging, is the Christ consciousness within, a mediating awareness that does not depend on birth or death because it was never made by them.
Melchizedek, king of righteousness and king of peace, has neither beginning of days nor end, standing for the deathless self already present in a person. The unbreakable oath marks an inner priesthood that endures while every outward form of worship rises and falls.
Priests without an oath: the mind's passing religious efforts, made and unmade with the body
Melchisedec: the deathless self within, priest without beginning or end, righteousness and peace joined