One of the most common ways to approach the issues of continuity and discontinuity regarding “law” in the Bible is to see a threefold, or tripartite, division: (a) moral, (b) civil, (c) ceremonial. The argument usually goes along the lines of saying that Christ fulfilled the civil and ceremonial aspects of the law (discontinuity), but that the moral law remains in effect (continuity).
There is a lot to commend in such an approach, but I don’t think it fully works. For example, the Sabbath command—surely part of the moral law in the OT—is never repeated in the NT and Paul seems to regard it a matter of some indifference (Rom. 14:5; Col. 2:16–17).
But that doesn’t mean that the three-fold division doesn’t have usefulness.
D. A. Carson has a brief, helpful, and nuanced comment about this issue in his important essay, “Mystery and Fulfillment: Toward a More Comprehensive Paradigm of Paul’s Understanding of the Old and New,” in The Paradoxes of Paul, vol. 2 of Justification and Variegated Nomism, ed. Carson, O’Brien, Seifrid (Grand Rapids: Baker, 2004), pp. 393–436. (For an excellent summary and outline of this essay, see this post by Andy Naselli.)
In short, the problem with the tripartite division of law, which as a device for explaining continuity and discontinuity between the Testaments, goes back to Thomas Aquinas,* is that it attempts to construct an a priori grid to sort out what parts of the law Christians must keep or do, and holds that Paul must have adopted some such grid, even if he does not explicitly identify it.
If instead we adhere more closely to Pauline terminology in this regard, we may still usefully speak of the tripartitc division from an a posteriori perspective: after we have observe the patterns of continuities and discontinuities that Paul establishes, those old covenant laws which Christians “fulfill” in a fashion most closely aligned with their function within the old covenant may safely be labeled “moral,” without fear that an a priori definition is domesticating Paul’s thought.
*This is not to deny that one can find the tripartite distinction in Origen, Jerome, and others. But Thomas was the one who fleshed out the tripartite structure as the fundamental basis for establishing the lines of continuity and discontinuity between the Testaments. (p. 429)