Portrait of idiot with crack (3,4)
I believe the answer is:
mug shot
'portrait' is the definition.
(thesaurus)
'idiot with crack' is the wordplay.
'idiot' becomes 'mug' (I've seen this before).
'with' says to put letters next to each other.
'crack' becomes 'shot' ('shot' can be a synonym of 'crack'**).
'mug'+'shot'='MUG SHOT'
'of' acts as a link.
(Other definitions for mug shot that I've seen before include "Passport photograph?" , "Photograph taken for police records" , "Police photo" , "police will want this from him" .)