Boss gets rid of one cook (4)
I believe the answer is:
chef
'cook' is the definition.
(both can mean someone who cooks)
'boss gets rid of one' is the wordplay.
'boss' becomes 'chief' (synonyms).
'gets rid of' suggests deleting specific letters.
'one' becomes 'i' (Roman numeral).
'chief' with 'i' taken away is 'CHEF'.
(Other definitions for chef that I've seen before include "who has a set of knives?" , "Professional cook" , "Principal cook" , "Key kitchen worker" , "Saucier" .)