Assuming that you are still speaking of the Law of Moses as a covenant, yes.
Since there's ambiguity here, let me clarify what I mean whenever I refer to the term 'law' - that way you could simply read without going through the trouble of constructing assumptions. Kindly bear with the slightly long post.
There are at least 3 usages of the word 'law' in scriptures -
Usage 1: In Matthew 5:17, it denotes the first 5 Books of the OT Scripture.
Usage 2: In Rom 13:10, it refers to the set of commandments given by Moses as seen from the preceding Rom 13:9.
Usage 3: In Rom 3:27, it refers to a single governing principle such as a "law" of gravity etc.
So when Paul declares we are no longer under the 'law'(Rom 6:14), he couldn't be meaning Usage 1 - for Scripture cannot be relegated.
Given his constant exhortation against following the OT commandments such as circumcision in Galatians etc. (Gal 5:3), we might be inclined to think he means Usage 2 - but that throws problems as well. Paul does refer to several OT commandments to be followed even now(Rom 13:9) and Acts 16:3 has Paul circumcising Timothy - which shows that the commandments themselves are not the issue - but as you said earlier, that depending on them for justification is the issue.
Which leads us to Usage 3 - that which is confirmed in Paul singling out 1 single principle in the OT to capture the entire concept of justification by the law - Lev 18:5. This is seen in him contrasting the "righteousness which is of the law" and the "righteousness which is of faith" by referring to this single principle in Rom 10:5. Again, the same contrast is done in similar fashion in Gal 3:12.
Hence, this Lev 18:5 is what he refers to as the "law of works" - which basically amounts to any variant of "I believe if I do a certain set of commandments, then I shall be justified/deemed righteous unto life in my having worked these".
So, whenever I refer to the "law" as being against it, it's simply this Lev 18:5 Law of works. I now can freely say I am no longer under the law(Usage 3) while still upholding the holiness of the
spiritual set of commandments(Usage 2).
And this law of works is applicable even today, and even among the non-jews - for what are concepts such as 'karma' if not a variant of Lev 18:5. Which is why Galatians and related texts are still relevant today. As an aside, I believe a lot of people in the church pews today hold a variant of this in their hearts where they believe it would be
because of their 'work' in believing or repenting that they will be saved.
However, Jesus revealed the correct understanding of those moral laws. God allowed things in Moses Law that are not allowed under the new covenant.
True. Which is why I believe that the Law(Usage 2) is now revealed Spiritually. Also, this Law of Christ is the law of liberty - not in that it permits us to forsake certain commandments, but in that it simplifies it into the royal laws to Love. In the OT, each had studied all the 613 commandments(?), and yet were diligent to ask one another and the teachers of the law if any act of theirs was in violation of any of the commandments. But what was the purpose or final end(1Tim 1:5) of any of these commandments(Usage 2 law) - to get us to Love and to show us through all our transgressions how we need a Saviour to get round to such Love.
But once we are in Christ, we do not need to be taught of one another(Jer 31:34) - God's law(Usage 2) is written in our hearts(Jer 31:33) - and it is God who causes us to walk in them(Eze 36:27, Php 2:13). We simply need to love and in that be assured we are not transgressors of any commandments of God. No burden of fearful checking against several checklists now. (Edit: ) And we love not in order to merit salvation - we love just because that's who we are in Christ.