Heb 2:15-17, 3:1, 4:14-15, 5:5-10, 6:20, 7:11-28
God made Aaron the high priest to judge the children of Israel. (Ex 28:29-30)
Ex 28:29 And Aaron shall bear the names of the children of Israel in the breastplate of judgment upon his heart, when he goeth in unto the holy place, for a memorial before the Lord continually. 30 And thou shalt put in the breastplate of judgment the Urim and the Thummim; and they shall be upon Aaron's heart, when he goeth in before the Lord: and Aaron shall bear the judgment of the children of Israel upon his heart before the Lord continually.
Jesus is the true High Priest without sin. (Heb 4:14-15, Heb 3:1)
Heb 4:14 Seeing then that we have a great high priest, that is passed into the heavens, Jesus the Son of God, let us hold fast our profession. 15 For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin.
Heb 3:1 Wherefore, holy brethren, partakers of the heavenly calling, consider the Apostle and High Priest of our profession, Christ Jesus;
Jesus is the Christ who faithfully did the work of the high priest to redeem us from our sins. (Heb 2:15-17)
Heb 2:15 And deliver them who through fear of death were all their lifetime subject to bondage. 16 For verily he took not on him the nature of angels; but he took on him the seed of Abraham. 17 Wherefore in all things it behoved him to be made like unto his brethren, that he might be a merciful and faithful high priest in things pertaining to God, to make reconciliation for the sins of the people.
God made Jesus, the Son of God, a priest in the order of Melchizedek. Although Jesus is the Son of God, He suffered to save us. (Heb 5:5-10, Heb 6:20)
Heb 5:5 So also Christ glorified not himself to be made an high priest; but he that said unto him, Thou art my Son, to day have I begotten thee. 6 As he saith also in another place, Thou art a priest for ever after the order of Melchisedec. 7 Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared; 8 Though he were a Son, yet learned he obedience by the things which he suffered; 9 And being made perfect, he became the author of eternal salvation unto all them that obey him; 10 Called of God an high priest after the order of Melchisedec.
Heb 6:20 Whither the forerunner is for us entered, even Jesus, made an high priest for ever after the order of Melchisedec.
The law could not perfect those who came to God, but Jesus is not a Levitical priest, but the high priest who forever perfected those who came to God from the tribe of Judah. (Heb 7:11-28)
Heb 7:11 If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron? 12 For the priesthood being changed, there is made of necessity a change also of the law. 13 For he of whom these things are spoken pertaineth to another tribe, of which no man gave attendance at the altar. 14 For it is evident that our Lord sprang out of Juda; of which tribe Moses spake nothing concerning priesthood. 15 And it is yet far more evident: for that after the similitude of Melchisedec there ariseth another priest, 16 Who is made, not after the law of a carnal commandment, but after the power of an endless life. 17 For he testifieth, Thou art a priest for ever after the order of Melchisedec. 18 For there is verily a disannulling of the commandment going before for the weakness and unprofitableness thereof. 19 For the law made nothing perfect, but the bringing in of a better hope did; by the which we draw nigh unto God. 20 And inasmuch as not without an oath he was made priest: 21 (For those priests were made without an oath; but this with an oath by him that said unto him, The Lord sware and will not repent, Thou art a priest for ever after the order of Melchisedec:) 22 By so much was Jesus made a surety of a better testament. 23 And they truly were many priests, because they were not suffered to continue by reason of death: 24 But this man, because he continueth ever, hath an unchangeable priesthood. 25 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them. 26 For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens; 27 Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself. 28 For the law maketh men high priests which have infirmity; but the word of the oath, which was since the law, maketh the Son, who is consecrated for evermore.