The "old" priesthood is no longer required.
Heb 7:12; For when the priesthood is changed, of necessity there takes place a change of law also.
All believers are priests now, there is no need for someone to do the sacrifices for us.
1 Pet 2:5 you also, as living stones, are being built up as a spiritual house for a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ.
1 Pet 2:9 But you are A CHOSEN RACE, A royal PRIESTHOOD, A HOLY NATION, A PEOPLE FOR God's OWN POSSESSION, so that you may proclaim the excellencies of Him who has called you out of darkness into His marvelous light;
All believers have access to the throne of grace now.
Heb 4:16; Therefore let us draw near with confidence to the throne of grace, so that we may receive mercy and find grace to help in time of need.
God split the veil of the temple in two, giving all believers access to him, there is no need to go through another man (priest)
Matt 27:51; And behold, the veil of the temple was torn in two from top to bottom; and the earth shook and the rocks were split.
Any sacrifices that an earthly priest does for you cannot be perfect.
Christ is the high priest, but we have access to him, not just other priests.
Heb 4:15; For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin.
Heb 5:10; being designated by God as a high priest according to the order of Melchizedek.
Heb 6:20; where Jesus has entered as a forerunner for us, having become a high priest forever according to the order of Melchizedek.
Heb 7:17; For it is attested of Him, "YOU ARE A PRIEST FOREVER ACCORDING TO THE ORDER OF MELCHIZEDEK."
Heb 7:22; so much the more also Jesus has become the guarantee of a better covenant.
Heb 7:23; The former priests, on the one hand, existed in greater numbers because they were prevented by death from continuing,
Heb 7:24; but Jesus, on the other hand, because He continues forever, holds His priesthood permanently.
To be a perfect priest, is one of the reasons Jesus came, to have other priests is kind of like saying "Jesus isn't really good enough", I'll let a man do it.
Heb 7:25; Therefore He is able also to save forever those who draw near to God through Him, since He always lives to make intercession for them.
Heb 7:26; For it was fitting for us to have such a high priest, holy, innocent, undefiled, separated from sinners and exalted above the heavens;
Heb 7:27; who does not need daily, like those high priests, to offer up sacrifices, first for His own sins and then for the sins of the people, because this He did once for all when He offered up Himself.
Heb 7:28; For the Law appoints men as high priests who are weak, but the word of the oath, which came after the Law, appoints a Son, made perfect forever.
Heb 8:1; Now the main point in what has been said is this: we have such a high priest, who has taken His seat at the right hand of the throne of the Majesty in the heavens,
In the old covenant, there was an inner sanctum, a "Holy of Holies" that people didn't have access to, not even priests had access to it, only the high-priest.
Heb 9:1 Now even the first covenant had regulations of divine worship and the earthly sanctuary.
Heb 9:2 For there was a tabernacle prepared, the outer one, in which were the lampstand and the table and the sacred bread; this is called the holy place.
Heb 9:3 Behind the second veil there was a tabernacle which is called the Holy of Holies,
Heb 9:4 having a golden altar of incense and the ark of the covenant covered on all sides with gold, in which was a golden jar holding the manna, and Aaron's rod which budded, and the tables of the covenant;
Heb 9:5 and above it were the cherubim of glory overshadowing the mercy seat; but of these things we cannot now speak in detail.
Heb 9:6 Now when these things have been so prepared, the priests are continually entering the outer tabernacle performing the divine worship,
Heb 9:7 but into the second, only the high priest enters once a year, not without taking blood, which he offers for himself and for the sins of the people committed in ignorance.
Heb 9:8 The Holy Spirit is signifying this, that the way into the holy place has not yet been disclosed while the outer tabernacle is still standing,
This is why the significance of the veil being rent in two is so important.
Heb 9:14; how much more will the blood of Christ, who through the eternal Spirit offered Himself without blemish to God, cleanse your conscience from dead works to serve the living God?
Heb 9:15; For this reason He is the mediator of a new covenant, so that, since a death has taken place for the redemption of the transgressions that were committed under the first covenant, those who have been called may receive the promise of the eternal inheritance.
Heb 9:16; For where a covenant is, there must of necessity be the death of the one who made it.
Heb 9:11; But when Christ appeared as a high priest of the good things to come, He entered through the greater and more perfect tabernacle, not made with hands, that is to say, not of this creation;
Heb 9:22; And according to the Law, one may almost say, all things are cleansed with blood, and without shedding of blood there is no forgiveness.
Heb 9:25; nor was it that He would offer Himself often, as the high priest enters the holy place year by year with blood that is not his own.
Heb 9:26; Otherwise, He would have needed to suffer often since the foundation of the world; but now once at the consummation of the ages He has been manifested to put away sin by the sacrifice of Himself.
Heb 9:28; so Christ also, having been offered once to bear the sins of many, will appear a second time for salvation without reference to sin, to those who eagerly await Him.
It is impossible for sacrifices of earthly priests to cleanse us.
Heb 10:1; For the Law, since it has only a shadow of the good things to come and not the very form of things, can never, by the same sacrifices which they offer continually year by year, make perfect those who draw near.
Heb 10:2; Otherwise, would they not have ceased to be offered, because the worshipers, having once been cleansed, would no longer have had consciousness of sins?
Heb 10:3; But in those sacrifices there is a reminder of sins year by year.
Heb 10:4; For it is impossible for the blood of bulls and goats to take away sins.
Only the sacrifice done by Christ can take away our sins.
Heb 10:11; Every priest stands daily ministering and offering time after time the same sacrifices, which can never take away sins;
No priests are required, we ourselves can enter the outer sanctum, the holy place!
Heb 10:19; Therefore, brethren, since we have confidence to enter the holy place by the blood of Jesus,
Heb 10:21; and since we have a great priest over the house of God,
Heb 10:26; For if we go on sinning willfully after receiving the knowledge of the truth, there no longer remains a sacrifice for sins,
Heb 10:31; It is a terrifying thing to fall into the hands of the living God.
We ourselves are priests, all believers are. We have access to the Holy Place, We have access to Christ our high-priest, we don't need a priest (who himself is imperfect)
to confess to, to offer sacrifices for us, or to talk to God for us.