Barnes, in his commentary, commented on the transition from OT to NT as, “but there is the bringing in of a better hope, by which we have access to God.” He mentioned that the Law could not do this because it still left a guilty conscience and the sin in their lives were never atoned for. Now we can be reconciled and approach God through the gospel – a better foundation for hope than what the Law could do. Being grounded in this hope, given through the gospel, we are now reconciled with God, can approach Him, and with full assurance know that He is ready to saves us.
Not the grace of hope; that is not something newly brought in, the saints under the Old Testament had it; nor is it better now than then, though it has greater advantages and more encouragement to the exercise of it: nor heaven and eternal glory, the thing hoped for; the saints under the legal dispensation hoped for this, as well as believers under the present dispensation; nor is what the latter hope for better than that the former did: nor is God the author and object of hope intended; the phrase of bringing in will not suit with him; besides, he is distinguished from it, in the next clause: to understand it of the Gospel, the means of hope, and of encouraging it, is no ill sense; that standing in direct contradistinction to the law: but the priesthood of Christ, of which the apostle is treating in the context, is generally understood, which is the ground of hope; for all promises respecting eternal life are confirmed by it, and all blessings connected with it procured; and it is better than the Aaronic priesthood, under the law; and a better ground of hope than the sacrifices of that law were: Christ himself may be designed, who is often called hope, being the object, ground, and foundation of it; and is a better one than Moses, or his law, Aaron, or his priesthood; and it is by him men draw nigh to God; and the bringing in of him or his priesthood shows that Christ’s priesthood was not upon the foot of the law, and that he existed as a priest, before brought in, and as a better hope, though not so fully revealed; and it may have respect to his coming in the flesh, being sent, or brought in by his father: now the bringing in of him and his priesthood did make something perfect; it brought to perfection all the types, promises, and prophecies of the Old Testament, the whole law, moral and ceremonial; it brought in perfect atonement, reconciliation, pardon, righteousness, and redemption; it perfected the persons of all God’s elect; and perfectly provided for their holiness, peace, comfort, and eternal happiness: some read the words “but it”, the law, “was the bringing in of a better hope”: the law led unto, made way for, and introduced. Christ, the better hope; and so the Arabic version, “seeing it should be an entrance to a more noble hope”; the Syriac version renders it, “but in the room of it entered a hope more excellent than that”; than the law. – Gill
There is, on the one hand, the abrogation of an earlier commandment because it was weak and ineffectual (for the law made nothing perfect); there is, on the other hand, the introduction of a better hope, through which we approach God – Hebrews 7:18-19