Despicable person taking head off fish (3)
I believe the answer is:
eel
'fish' is the definition.
(eel is a type of fish)
'despicable person taking head off' is the wordplay.
'despicable person' becomes 'heel' (old-fashioned term for a horrible person).
'taking head off' means to remove the first letter.
'heel' with its first letter taken away is 'EEL'.
(Other definitions for eel that I've seen before include "Creature like conger or moray" , "Large elver" , "slipper" , "A sea snake" , "Conger, e.g." .)