A puzzle for the Inspector (5)
I believe the answer is:
rebus
This clue is a double definition.
'a puzzle' is the first definition.
(type of visual puzzle)
'inspector' is the second definition.
(I know that Rebus is a inspector)
'for the' is the link.
(Other definitions for rebus that I've seen before include "Word puzzle involving pictures" , "solver?" , "Word-picture puzzle" , "Visual type of word puzzle" , "Picture-letter puzzle" .)