who has become a priest, not on the basis of a legal requirement concerning bodily descent, but by the power of an indestructible life.
This is a different kind of priesthood than the one set up by Aaron. It is based on an oath from God and an indestructible [immortal] life. Not on a physical association by birth within the tribe of Levi.
Psalm 110:4 The LORD has sworn and will not change his mind: "You are a priest forever, in the order of Melchizedek."
Hebrews 7:11 If perfection could have been attained through the Levitical priesthood (for on the basis of it the law was given to the people), why was there still need for another priest to come--one in the order of Melchizedek, not in the order of Aaron?
We see Jesus as the first example of this type of priest, coming out of the tribe of Judah which produces Kings not priests. Hence it is a royal priesthood, as Jesus was both King and Priest.
But you are a chosen people, a royal priesthood, a holy nation, a people belonging to God, that you may declare the praises of him who called you out of darkness into his wonderful light. 1 Peter 2:9
This is God's plan for his chosen people, that they will enter into the Melchizedek order of priesthood, based on an endless life.
Exodus 19:6 you will be for me a kingdom of priests and a holy nation.' These are the words you are to speak to the Israelites."
We see Moses fulfilling this function as a shadow of the priesthood to come, when he talks to God face to face on behalf of God's chosen people. And, we learn the function he assumes is more than as an earthly priest.
And the LORD spake unto Moses face to face, as a man speaketh unto his friend.