Sin in the AV is said to be “the transgression of the law”. Believers though, are not under the law, (nor are gentiles) so they can’t “transgress it”. Later translations say that sin is “lawlessness”, as being without law. Without law really means without control or standards. To be of natural origin without modification.
When people are placed under obligation to perform to a standard which they then fail, they become aware of that failure, if they knew they were under that obligation. Then it becomes a matter of how authoritative was the source of this required standard, as to how much trouble you are in. The Mosaic law had severe penalties for some things.
Sin though, may best be described as guilt? Or consciousness of guilt? After all, if you are unaware of your guilt it will have no effect on you until and if someone else hits you with a penalty. (speeding fine?). Even if the particular law had little or no authority, just the fact of you being aware of it places you in a state of stress or tension over whether there will be a penalty, how bad it may be and just when it may hit you. [Some cultures may have laws that are morally wrong yet still carry penalties and guilt].
This is why it says where there is no law there is no transgression, not that there IS necessarily no law, but just that if you did not know about it you were not considered guilty of it in terms of penalty for it. Then again some people may have an exaggerated sense of their guilt for various reasons.
Sin tends to be indefinable once you get to the believer stage. Believers are said “not to sin” (John) [which contradicts the “if we say we have no sin…” but context there may suggest pre-Christianity. It also says “but if they DO sin…” they have an advocate. The Spirit is said to be grieved, rather than pointing to some specific legal transgression. The obliteration of guilt through the body of Jesus on the cross then places one inside a relationship where any supposed sin and guilt exist as hypothetical stresses in an otherwise perfect love relationship.
Legalistic interpretation of transgression or sin would be that which goes against, or is outside of, God, his being, purpose and action. Which simply means something less than love. For God’s purposes, any retention of the guilt which he removed by the cross, for you, amounts to sin.
[God’s conscience should be your conscience] [And then again, all sin was borne by Jesus]