You will here some say in the Reformed world that the Mosaic Administration is a republication of the Covenant of Works, citing most effectively Leviticus 18:5 (“So you shall keep My statutes and My judgments, by which a man may live if he does them; I am the LORD.”) and other places where it seems that obedience to the Law as given by Moses is the requirement for the Lord’s blessing and therefore life. However I believe that one can cite the same verses and make the opposite notation, that the Law being an administration of the Second Covenant, the Covenant of Grace, is not a Covenant of Works because most strikingly that which a Covenant of Works is cannot be fulfilled by the Mosaic Covenant. So there is I think a definitional mistake by categorizing the Mosaic administration in any part of a Covenant of Works because in doing so it presupposes that one can follow the Law to receive salvation like Adam (even if such a thing were possible, which it is not), who was first under the Covenant of Works for salvation and failed. Since Adam failed the probationary test we cannot now fulfill the requirements of this covenant and since according to Romans 5 the curse of this failure continues in us since Adam was our covenantal head it would therefore not make sense that God would put is again under a covenant which had been broken by Adam’s disobedience (and our disobedience in Adam). Especially since we continue under its curse. The Covenant of Works had already been abrogated, why would/should it be instituted again by the Mosaic administration since we who are descendants of Adam were already condemned? It seems to be unnecessary to put us again under condemnation a second time.
The Westminster Confession of Faith Chapter 7, sections III, IV, & V makes clear that the Law (or Mosaic covenant) is an administration of the Covenant of Grace.
Chapter 7 –
Of God’s Covenant with Man.
III. Man by [Adam’s] fall having made himself incapable of life by that covenant, the Lord was pleased to make a second, commonly called the covenant of grace: wherein he freely offered unto sinners life and salvation by Jesus Christ, requiring of them faith in him, that they may be saved, and promising to give unto all those that are ordained unto life, his Holy Spirit, to make them willing and able to believe.
IV. This covenant of grace is frequently set forth in the Scripture by the name of a testament, in reference to the death of Jesus Christ, the testator, and to the everlasting inheritance, with all things belonging to it, therein bequeathed.
V. This covenant was differently administered in the time of the law, and in the time of the gospel: under the law it was administered by promises, prophecies, sacrifices, circumcision, the paschal lamb, and other types and ordinances delivered to the people of the Jews, all fore-signifying Christ to come, which were for that time sufficient and efficacious, through the operation of the Spirit, to instruct and build up the elect in faith in the promised Messiah, by whom they had full remission of sins, and eternal salvation, and is called the Old Testament.
You see in section V that the Divines at least believed the Law (thereby meaning the) is just a special administration of the Covenant of Grace. While administered differently than “in the time of the gospel” it still is part of the Second Covenant, or the Covenant of Grace.