“For the law brings wrath, but where there is no law there is no transgression.” -Romans 4:15
Paul is here confirming what he was previously explaining (verses13-14), but now in terms of the contrary effect the law has on fallen man.
The ultimate end of the law for fallen man is wrath, not grace. When the law is not present, Paul does not mean man stops sinning or that man’s sin doesn’t offend God, but that his sin is not as apparent and therefore not willfully or blatant.
When the law is present it teaches man what pleases God and displeases God. And once he knows the boundaries eternally fixed by God (parabasis translated transgression means to violate a boundary) and yet willfully and knowingly sins still, he stirs up the wrath of God—the true and just judgment of the holy Creator.
To illustrate, it’s the difference between a hunter who is hot on the trail of his game and accidentally wanders on to private property and harvests his animal versus the hunter who also hot on the trail of his game, enters the private property at place where a ‘no trespassing sign’ has been posted and harvests his animal. The former who transgressed ignorantly may still be cited for his violation (and had he known it was private property may still have chosen to cross but since there was nothing posted it cannot be known) but the latter who knew he was about to violate the law and then did so knowingly and willfully will be held to a higher account of his crime.