For this is the covenant I will make with the house of Israel after those days, declares the Lord. I will put My laws in their minds and inscribe them on their hearts. And I will be their God, and they will be My people.
10 For this is the covenant that I will make, etc. There are two main parts in this covenant; the first regards the gratuitous remission of sins; and the other, the inward renovation of the heart; there is a third which depends on the second, and that is the illumination of the mind as to the knowledge of God. There are here many things most deserving of notice.
In this part of the chapter, the apostle illustrates and confirms the superior excellency of the priesthood of Christ above that of Aaron, from the excellency of that covenant, or that dispensation of the covenant of grace, of which Christ was the Mediator (Heb 8:6): his ministry is more excellent, by how much he is the Mediator of a better covenant.
Commenting on Hebrews 8:6-13
For this is the covenant that I will make with the house of Israel,.... That is, this is the sum and substance of the covenant, which God promised to make with, or to make manifest and known to his chosen people, the true Israelites, under the Gospel dispensation; or the following are the several articles of that covenant, he proposed to consummate or finish, as...