Person in charge getting rid of one cook (4)
I believe the answer is:
chef
'cook' is the definition.
(chef is a kind of cook)
'person in charge getting rid of one' is the wordplay.
'person in charge' becomes 'chief' (I've seen this before).
'getting rid of' suggests deleting specific letters.
'one' becomes 'i' (Roman numeral).
'chief' with 'i' removed is 'CHEF'.
(Other definitions for chef that I've seen before include "Kitchen head" , "French master" , "Chief male cook in restaurant" , "Key kitchen worker" , "Saucier" .)