Cost of hiring detective is criminal (6)
I believe the answer is:
pirate
'is criminal' is the definition.
(I know that pirate is a type of thief)
'cost of hiring detective' is the wordplay.
I cannot quite understand how this works, but
'cost' could be 'rate' (rate is a kind of cost) and 'rate' is found in the answer.
'detective' could be 'pi' (private eye) and 'pi' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for pirate that I've seen before include "Copyright infringer" , "plagiarist" , "Run off without permission" , "Cornishman maybe" , "Hook", for example" .)