“And what we have said is even more clear if another priest like Melchizedek appears, one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life. For it is declared: “You are a priest forever, in the order of Melchizedek” ( Hebrews 7:15-17 )
The Levitical priesthood was a lifetime position. Once a person became High Priest this position was retained until death ( Numbers 35:25 ). However, each time the priest died a new priest would be appointed, so in another sense you might say this priesthood never had any permanence, death always interrupted it.
Jesus’ priesthood greatly contrasts this because death could not hold him captive and therefore the grave did not interrupt His appointment as High Priest. His resurrection from the dead, solidified this position permanently. “For we know that since Christ was raised from the dead, he cannot die again; death no longer has mastery over him” ( Romans 6:9 ). Since the priesthood is a lifetime position, Jesus’ resurrection guarantees that He eternally holds this position. “Now there have been many of those priests, since death prevented them from continuing in office; but because Jesus lives forever, he has a permanent priesthood. Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them” ( Hebrews 7:23-25 ).
This is good news for us because it means the sacrifice made for sin worked, the first and only time it was given. In other words the payment for sin completely wiped out and nullified the debt that sin created. Which is why death had no power to hold Jesus captive, the account had been settled and closed, permanently. And if the power of sin and death had no claim to Jesus after He died, it also means that it can hold no power over Him while he’s alive. Therefore we know that Christ will live eternally. In the same way the power of sin is also broken over us who put saving faith in Jesus ( Hebrews 7:24, Hebrews 9:12, Hebrews 9:14, Hebrews 10:10, Hebrews 10:14, Hebrews 10:18 ).
“For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance—now that he has died as a ransom to set them free from the sins committed under the first covenant” ( Hebrews 9:15 ).
All of this becomes clear when we understand that Jesus is after a completely different line than what was established through the Levitical priesthood. The book of Hebrews records four times that Jesus became our High Priest fashioned after the order and with the rank of Melchizedek ( Hebrews 5:10, Hebrews 7:11, Hebrews 7:15, Hebrews 7:21 ). This is extremely significant because Melchizedek had no record of beginning or end. The beginning of Hebrews 7 records “like the Son of God he remains a priest forever” ( Hebrews 7:3 ). It had nothing to do with ancestry but everything to do with the power required to sustain life indefinitely. Jesus holds this power which is why there has been a change in priesthood ( Hebrews 7:11 ) and subsequently a change in the law ( Hebrews 7:12 ).