Chris Matthew provides his understanding of Gal. 3:21-25 and whether it teaches the Law has any authority for Christians:
Gal. 3:21-25 does not conflict with the theonomic position. Paul teaches us Christians that we are to receive the promise by faith and thus should not desire to be under the law as a way of justification lest we fall from grace (Gal. 3:2, 6-14, 24-26; 4:21; 5:4). We are no longer required to keep the outward form of the ceremonial (i.e., purely typological) law.
i.) First, this is supported by the historical context. Unbelieving Jews had not recognised as yet the dramatic change brought in by the redemptive realities of the New Testament. Although Christ had realised all that the Mosaic ceremonial law had anticipated, unbelieving Jews continued to follow these rituals. Paul set out to correct these errors.
ii.) Second, this interpretation is evident from the phrasing of the passage. Galatians 3 refers to shadows and realisations. Paul was speaking of that portion of the Mosaic law which was immature (Gal. 4:1-3), but which directed “unto Christ for justification by faith” (3:24). Since the moral law does not show the way of redemption or foreshadow the justifying work of Christ, we must conclude that Paul was referring to the foreshadows contained in the ceremonial law, which fit the description of an undeveloped (immature) system of principles which nevertheless led to the truth of justification by faith in Christ. These are the ordinances which were laid aside “when [the object of] faith came” (Gal. 3:19, 25), as the New Testament confirms elsewhere.
iv.) Finally, we know that Scripture interprets Scripture. If the critic of theonomy chooses to not recognise the moral/ceremonial distinction in the passage, then one renders the New Testament scriptures contradictory with respect to the Old Testament law. Paul declares that the law is holy, good, and something to be delighted in (Rom. 7:12, 22), and yet elsewhere that the law (in another sense, obviously) is a tutor that we are no longer under (cf. 1 Cor. 9:20-21).
Alternative interpretations of the passage are untenable in light of redemptive theology, the textual context, the historical backdrop, and the contradictions engendered.