Calvin gives a helpful summary in his commentary on the "four last books of Moses". Here are some excerpts from "The Use of the Law"...
1. Regarding the continuing use of the Law as "the rule of living well and righteously", after finding justification in Christ and being regenerated by the Spirit
Hence it appears that it is expedient for them to be slain by the Law, and that the death which it inflicts is life-giving. And this occurs in two ways; for, first, being stripped of the false opinion of their righteousness, wherein they prided themselves, they begin to seek in Christ what they mistakenly supposed might be found in themselves, so as to please God by gratuitous reconciliation, whereas they had previously sought to propitiate Him by the merit of their works; secondly, they learn that they are not sufficient to perform a single tittle of the Law, unless, being regenerated by God’s Spirit, they who were the slaves of sin live unto righteousness. And hence, in fine, the utility and fruit of the teaching of the Law proceeds; for, until we are renewed and God has given us hearts of flesh instead of hearts of stone, in vain are precepts dinned in our ears, since in our natural depravity we cordially reject them; but when He has engraved His law within our hearts, its outward instruction also profits us; for He so governs His children by the Spirit of reconciliation, as at the same time to will that they should be attentive and obedient to His voice. Still, because they are always far from attaining to perfect observance of it, they not only learn from it what is right, but also that they have need of His gratuitous mercy, that they may please Him through indulgence and grace, although they are still conscious of much infirmity.2. Regarding how Paul seems to abrogate the Law, and speaks of discontinuities, when contrasting the Gospel with a Judaism that rejects Christ
Further, because Paul seems to abrogate the Law, as if now-a-days it did not concern believers, we must now see how far this is the case. And, first, indeed, it is easy to perceive that he does not treat of the Law in the abstract, but sets it forth invested with those of its qualities, wherein it is opposed to the Gospel; for, inasmuch as his controversy was with those who interpreted it amiss, he could not help contrasting the Law with the Gospel, as if they were in opposition to each other: not that they were really so, if their respective doctrine be dexterously applied to its proper object, but because such a conflict arose from the absurd mixture, which the false apostles introduced. They asserted that men are justified by the works of the Law, and, if this were admitted, the righteousness of faith was destroyed, and the Gospel fell to the ground. They, moreover, restored the yoke imposed on the ancient people, as if no liberty had been obtained by the blood of Christ. In this discussion it was necessary for Paul to advert only to that which is peculiar to Moses, and distinct from Christ; for although Christ and Moses perfectly accord in the substance of their doctrine, still, when they are compared with each other, it is fitting to distinguish what is peculiar to each. In this respect Paul calls the Law “the letter,” because Moses had no other charge than to speak in the name of God, (2 Corinthians 3:6;) and this in itself is not only useless, but also deadly; for when the word resounds in the ears only, it produces nothing but condemnation. Besides, he considers the Law as connected with promises and threatenings. Whence it follows, that salvation can only be procured by it if its precepts be exactly fulfilled. Life is indeed promised in it, but only if whatever it commands be complied with; whilst, on the other hand, it denounces death against its transgressors, so that to have offended in the slightest point is enough to condemn and destroy a person; and thus it overwhelms all men with despair. Lastly, because the ceremonies by which God prepared His ancient people as by puerile and elementary instruction for the faith of the Gospel, were annexed to the Law, Paul embraces those also in his comparison between the Law and the Gospel. Hence it follows that, in so far as Moses is distinguished from Christ, his ministration has ceased, although his embassy was identical with that which Christ afterwards discharged. As regards the ceremonies, we must consider that an end was put upon them by Christ’s coming, in such a way as to establish their truth more firmly than as if they still remained in use: for we acknowledge that in them, as in a mirror, was formerly shewn to the Fathers, what is now displayed to us in its reality. Whence it appears that they are greatly mistaken who altogether reject as useless that instruction which we read in the writings of Moses; and that the squeamishness of those who despise it is also intolerable.At the end, Calvin also helpfully refers back to further treatment in his Institutes: "Let my readers seek in the Second Book of my Institutes, Chapter 7., what further tends to the explanation of this subject."
