A crime? Yes, when there's no love lost! (3)
I believe the answer is:
sin
'a crime?' is the definition.
(thesaurus)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for sin that I've seen before include "Lapse against moral law" , "Moral offence" , "Breach of morality" , "Something wrong" , "Wrongdoing" .)