The Forerunner, Jesus, has entered for us, having become forever a High Priest according to the order of Melchisedec. Heb 6.
Who has been appointed not according to the law of a fleshy commandment but according to the power of an indestructible life. For it is testified, 'You are a Priest forever according to the order of Melchisedec.'...By so much Jesus has also become the surety of a better covenant. Heb 7.
Concerning His Son, who came out of the seed of David according to the flesh, who was designated the Son of God in power according to the Spirit of holiness out of the resurrection of the dead, Jesus Christ our Lord. Rm 1.
It is necessary that this One also have something which He may offer...Now then if He were on earth, He would not be a Priest at all, there being those who offer the gifts according to the law, who serve the example and shadow...But now He has obtained a more excellent ministry inasmuch as He is also the Mediator of a better covenant, which has been enacted upon better promises. Heb 8.
The way of the Holy of Holies has not yet been manifested while the first tabernacle still has its standing...[T]hrough His own blood, entered once for all into the Holy of Holies, obtaining an eternal redemption...How much more will the blood of Christ, who through the eternal Spirit offered Himself without blemish to God, purify our conscience from dead works to serve the living God? And because of this He is the Mediator of a new covenant, so that, death having taken place for redemption of the transgressions under the first covenant, those who have been called might receive the promise of the eternal inheritance. For where there is a testament, the death of him who made the testament must of necessity be established. For a testament is confirmed in the case of the dead, since it never has force when he who made the testament is living ...Nor in order that He might offer Himself often, just as the high priest enters into the Holy of Holies year by year by the blood of other creatures; since then He would have had to suffer often since the foundation of the world. But now once at the consummation of the ages He has been manifested for the putting away of sin through the sacrifice of Himself...So Christ also, having been offered once to bear the sins of many, will appear a second time to those who eagerly await Him, apart from sin, unto salvation. Heb 9.
Therefore, coming into the world, He says, 'Sacrifice and offering You did not desire, but a body You have prepared for Me.'...'I have come to do Your will.' He takes away the first that He may establish the second...[T]his One, having offered one sacrifice for sins, sat down forever on the right hand of God...'This is the covenant which I will covenant with them after those days, says the Lord: I will impart My laws upon their hearts, and upon their mind I will inscribe them'...Now where forgiveness [of their sins and their lawlessnesses (plural)] is, there is no longer an offering for sin. Having therefore, brothers, boldness for entering the Holy of Holies...which entrance He initiated for us as a new and living way through the veil...And having a great Priest over the house of God... Heb 10.
Jehovah declares to my Lord, Sit at My right hand until I make Your enemies Your footstool...Jehovah has sworn, and He will not change: You are a Priest forever according to the order of Melchizedek. Psa 110.
For there is one God and one Mediator of God and men, the man Christ Jesus. 1 Tim 2.
Jesus, the Mediator of a new covenant. Heb 12.
Christ Jesus became a high priest according to the order of Melchisedec (not according to the order of Aaron) when He, Christ, resurrected from the dead. Not before. In resurrecting and in resurrection, He brought humanity, His humanity, even His body, into God fully and 'officially' (cf Mt 16:27--17:2, 9). Which, as a man, as the GodMan and as the ManGod, qualifies Him to be the High Priest of a new covenant. The covenant (testament) of having provided an eternal redemption for the goal to be a minister (imparter) of Himself into and to His receivers both now, in this life, and forever (Jn 1:12; Rv 22:1, 14, 17). Just as Melchisedec, the priest and king of [Jeru]Salem ministered, in type (typology) bread and wine to Abraham in Genesis 14.