Police photo of cup's stolen (3,4)
I believe the answer is:
mug shot
'police photo' is the definition.
(I've seen this before)
'cup's stolen' is the wordplay.
'cup's' becomes 'mugs' (I can't justify this - if you can you should give a lot more credence to this answer).
'stolen' becomes 'hot' (stolen goods are 'hot').
'mugs'+'hot'='MUG SHOT'
'of' is the link.
Can you help me to learn more?
(Other definitions for mug shot that I've seen before include "police will want this from him" , "Photograph taken for police records" , "Passport photograph?" , "Police photo" .)