Hebrews 7 tells us that God declared a decree in Psalm 110 to the seed of David that He would be a priest forever according to the order Melchizidek. Hebrews 8 argues that since according to the Aaronic priesthood you had to be of Levi to a be a priest (and Christ is of Judah), there had to be a change in the law to accommodate a New Priesthood. The argument Hebrews is making is not that the Church is under the New Covenant, but that the Law of Moses with its priesthood and sacrifices has passed away, replaced by Christ, who is the mediator of all the covenants.
Again the purpose of Hebrews is to tell Jewish believers in Christ that they need to make a firm decision to stand with Christ. The Temple was still standing, and the priests were still offering sacrifices according to the Mosaic law. Furthermore, the church in Jerusalem was apparently still meeting in the temple and James and the brothers even attempted to get Paul to take a vow to show that he had not “apostatized from Moses” but walked orderly “keeping the law” (Acts 21:21,24). This created much confusion for the Jewish Believers, and Hebrews is written to show them that their own scriptures and prophets told them that the Law would eventually be replaced.
However, in establishing the ground for the High Priesthood of Melchizidek, Hebrews does not appeal to Israel’s New Covenant, but to the decree that the Father made to the Son in Psalm 110. His High Priesthood comes not according to the law of a carnal commandment, but emerges from His place in resurrection as the Seed of David who was declared to be the Son of God with Power by the resurrection from the dead (Rom 1:3-4), and is said to be in the “power of an incorruptible life” (Heb 7:16) His priesthood comes out of His Sonship, not out of the New Covenant with Israel that He mediates.
Hebrews 1:5 and Hebrews 7:17; reference two decrees that are made directly to the Son from the Father from Psalm 2 and Psalm 110. These two decrees establish His eternal throne and His inheritance of all the nations to rule them with a rod of Iron (Psalm 2:6-9) and His High Priesthood (Psalm 110:4). The Psalmist was referring by inspiration to something that God said to the Son Himself, and these are aspects of the Everlasting Covenant the Father made with Jesus the great Shepherd of the Sheep, referred to in Hebrews 13:20.
It is based on this declaration that He is our High Priest (for the church), can save us to the uttermost (Heb 7:25) (by His life) and will eventually make us kings and priests as He Is (rev 5:10). We believe these declarations are aspects of the Everlasting Covenant between the Father and the Son.