J. N. Darby wrote an article titled, "The Sabbath: or, Is the law dead, or am I?". That's a good question to contemplate.
To be blunt, a lot of dispensationalists get this one wrong. We tend to think the Law was "for then", not "for now". But that's not what Scripture actually teaches. Scripture teaches not that the Law came to an end, but that our death with Christ has made us dead to it. This perspective is important if we want to understand what the Epistles (particularly the Pauline Epistles) teach.
Romans 7:5–8 is careful to tell us two things that almost appear to be opposites. First, when we attempt to keep the Law, we will find that it merely empowers the sin that lives in us (Romans 7:18–23 reiterates this point). Many Christians talk about the Law curbing our tendency to sin, but the Epistles tell us just the opposite: the Law makes it easier for us to sin!
The second lesson in Romans 7:5–8 is that while the Law provides a point of attack for the sin that lives in us, the problem is not that the Law is bad. On the contrary, the Law is holy and just and good (Romans 7:12). How does something that is holy and just and good have such a terrible effect on us?
The answer is in Romans 3:20, "by the Law is knowledge of sin." The Law was given to reveal sin (not, as J. N. Darby points out, sins). The Law does exactly what it was designed to do: it reveals our own sinfulness to us. It's working exactly as designed when it shows us to be sinners. This is why 1 Timothy 1:8–11 asserts that the Law isn't for righteous men, but unrighteous ones. The whole point of it is to reveal unrighteousness.
It is not the Law that has died, but I that have died. The problem isn't that the Law is bad, but that I am. And if I insist on putting myself under it, it will do exactly what God gave it to do: it will reveal that I am a sinner.
So what should I do? I need to accept what God has said: I have died with Christ. In that death, I have been put in a place where the Law has nothing to say to me. I have been separated from it as completely as I have been separated from sin. I have died to both, and I am to see myself in that light. My self-image is supposed to be "one that has died with Christ." That death removes me from sin, and from the Law.
Scripture doesn't teach that sin has died, but that I have died. Scripture doesn't teach that the Law has died, but that I have died. The disruption is on my side.
The Law is still as much in effect as it ever was. And it still works: it still shows fallen men and women to be sinners. We don't believe that the Law has been abolished, but that we have been separated from it by the death of Christ, so that we can be fruitful towards God (Romans 7:4).