Appointed members of the Old Testament Levitical priesthood were finite creations of God. They continually needed to be replaced because of physical death. These men were limited by the confines of age. The High Priests of the Jewish community needed to repeatedly offer the blood of sacrificed lambs and goats to temporarily stay off the wrath of God. The offerings presented by these men were not perfect. The customs of the Law were only a shadow of the greater things to come. They prefigured the arrival of a newer and better Covenant, which is the fulfillment of the Old Covenant. In other words, the entire Old Testament sacrificial system pointed to the single perfect atonement sacrifice performed by Jesus Christ at Calvary.
The Old Testament priests were sinners in need of redemption, just like the rest of us. Jesus is the pure, unblemished High Priest who offered Himself as a sacrifice for sin. He is the Source of everlasting life (Hebrews 5:9). Because of what He has done for us, we are able to approach God with confidence in His promises (Hebrews 4:14-16). Christ can sympathize with us because He took on human flesh. We have constant access to the grace of God because of His work. We can rest secure in Him, since He is perfectly reliable. He does not have any of the weaknesses that Jewish priests had. His priestly ministry is infinitely superior to that of the Old Testament priesthood.