Only those of the tribe of Levi and descendants of Aaron are allowed to be priests in Israel. Jesus is from the tribe of Judah, the kingship tribe. But a prophecy in Psalm 110 indicates that David’s son will be a priest after the order of Melchizedek (v.4).
Melchizedek was the king of Salem (original name for Jerusalem) and a “priest of God Most High” (Genesis 14:18). After Abram’s rescue of his nephew Lot through a hard fought battle, Abram met Melchizedek (whose name means “king of righteousness”) and paid a tithe or tenth of the spoils of the battle to him.
The author of Hebrews notes that no account is given of the birth or death of Melchizedek, which symbolizes his “eternal” priesthood, and notes that God would not have instituted a new priesthood order if the Aaronic priesthood had been sufficient to bring about eternal forgiveness. Jesus is an eternal priest by the resurrection from the dead and he has presented his offering, himself, in the heavenly tabernacle, after which the earthly one was modeled (see Hebrews 7-10).
Jesus is, therefore, the ultimate priest of Israel, and now for the whole world. He has the freedom now to sit down (Aaron and his offspring were not allowed to sit in the tabernacle) because his sacrifice, unlike the animal sacrifices, has perfected those cleansed by it forever. No more sacrifice is needed.
“Therefore, since we have a great high priest who has gone through the heavens, Jesus the Son of God, let us hold firmly to the faith we profess” (Hebrews 4:14). Jesus was tempted in every way like us but did not sin. Therefore he is the perfect priest and the spotless sacrifice, who can both identify with our weaknesses and be our substitute. Because he died, we don’t have to. He has so thoroughly satisfied the righteous demands of God that we can come boldly to the throne of God and receive His grace and help whenever we need it (Hebrews 4:16).
Jesus, as priest, has ended the need for animal sacrifices forever, and the need for the Day of Atonement as a festival in Israel, and has cleansed us from a guilty conscience once and for all by his sacrifice. He remains in heaven as our advocate (1 John 2:1) and constantly intercedes for us with the Father when Satan accuses us of sin (Revelation 12:10; Hebrews 7:25).
Related Articles
- How could Jesus legitimately be our high priest? (askthepastors.wordpress.com)
- Why do you think God required the blood of an animal for atonement of sin? (askthepastors.wordpress.com)
A Thimble-full of Theology for Daily Living 
Posts like this bregithn up my day. Thanks for taking the time.