Christ is the perfect priest or mediator between God and man because, as Son of God made man, he sums up in himself divinity and humanity. He was not only the Priest but also the Victim because he offered himself to be crucified for the sins of mankind to the Father. At the moment of his death the curtain of the temple, that is, the entrance into the Holy of Holies was torn in two from top to bottom signifying that the way to God the Father was now open for all mankind.
St. Paul compares the Atonement of the Old Covenant with the Atonement of Christ thus:
"But when Christ came as high priest of the good things that have come to be, passing through the greater and more perfect tabernacle not made by hands, that is, not belonging to this creation, he entered once for all into the sanctuary, not with the blood of goats and calves but with his own blood, thus obtaining eternal redemption. (Hb 9:1-13)
Although the Priesthood of the Old Covenant prefigured Christ, Christ did not belong to the Levitial priesthood because it had its limitations. Christ belonged to the priesthood of Melchizedeck, King of Salem, because he is presented "Without father, mother, or ancestry, without beginning of days or end of life, thus make to resemble the Son of God." (Hb 7:3) St. Paul follows this up by describing the priesthood of Christ as far superior to the Levitical priesthood as follows:
priests were many
because they were prevented by death from remaining in office,
but he, because he remains forever, has a priesthood that does not pass away.
Therefore, he is always able to save those who approach God through him,
since he lives forever to make intercession for them.
It was fitting that we should have such a high priest:
holy, innocent, undefiled, separated from sinners, higher than the heavens.
He has no need, as did the high priests, to offer sacrifice day after day,
first for his own sins and then for those of the people;
he did that once for all when he offered himself." (Hb 7:23-27)