Crime very associated with diamonds (4)
I believe the answer is:
vice
'crime' is the definition.
(vice crime is a kind of crime)
'very associated with diamonds' is the wordplay.
'very' becomes 'v' (abbreviation).
'associated with' says to put letters next to each other.
'diamonds' becomes 'ice' (I've seen this before).
'v'+'ice'='VICE'
(Other definitions for vice that I've seen before include "Bad habits" , "Immorality; clamping device" , "Moral weakness" , "Is the gripping tool evil?" , "Getting a grip" .)