This'll catch offenders in fine art crime (5,4)
I believe the answer is:
radar trap
'offenders in fine art crime' is the definition.
The definition suggests a singular noun which matches the answer.
'this'll catch' is the wordplay.
'this'll' becomes 'radar' (I am not sure about this - if you are sure you should believe this answer much more).
'catch' becomes 'trap' (trapping is a kind of catching).
'radar'+'trap'='RADAR TRAP'
Can you help me to learn more?
(Other definitions for radar trap that I've seen before include "enforcement mechanism" , "a catch, if one's too quick!" , "Changed to be more spiritual" .)