Complete Commentary on the Whole Bible, by Matthew Henry, at sacred-texts.com
(Heb 8:1-6) The excellence of Christ's priesthood above that of Aaron is shown.
(Heb 8:7-13) The great excellence of the new covenant above the former.
The substance, or summary, of what had been declared was, that Christians had such a High Priest as they needed. He took upon himself human nature, appeared on earth, and there gave himself as a sacrifice to God for the sins of his people. We must not dare to approach God, or to present any thing to him, but in and through Christ, depending upon his merits and mediation; for we are accepted only in the Beloved. In all obedience and worship, we should keep close to God's word, which is the only and perfect standard. Christ is the substance and end of the law of righteousness. But the covenant here referred to, was that made with Israel as a nation, securing temporal benefits to them. The promises of all spiritual blessings, and of eternal life, revealed in the gospel, and made sure through Christ, are of infinitely greater value. Let us bless God that we have a High Priest that suits our helpless condition.
The superior excellence of the priesthood of Christ, above that of Aaron, is shown from that covenant of grace, of which Christ was Mediator. The law not only made all subject to it, liable to be condemned for the guilt of sin, but also was unable to remove that guilt, and clear the conscience from the sense and terror of it. Whereas, by the blood of Christ, a full remission of sins was provided, so that God would remember them no more. God once wrote his laws to his people, now he will write his laws in them; he will give them understanding to know and to believe his laws; he will give them memories to retain them; he will give them hearts to love them, courage to profess them, and power to put them in practice. This is the foundation of the covenant; and when this is laid, duty will be done wisely, sincerely, readily, easily, resolutely, constantly, and with comfort. A plentiful outpouring of the Spirit of God will make the ministration of the gospel so effectual, that there shall be a mighty increase and spreading of Christian knowledge in persons of all sorts. Oh that this promise might be fulfilled in our days, that the hand of God may be with his ministers so that great numbers may believe, and be turned to the Lord! The pardon of sin will always be found to accompany the true knowledge of God. Notice the freeness of this pardon; its fulness; its fixedness. This pardoning mercy is connected with all other spiritual mercies: unpardoned sin hinders mercy, and pulls down judgments; but the pardon of sin prevents judgment, and opens a wide door to all spiritual blessings. Let us search whether we are taught by the Holy Spirit to know Christ, so as uprightly to love, fear, trust, and obey him. All worldly vanities, outward privileges, or mere notions of religion, will soon vanish away, and leave those who trust in them miserable for ever.