Head cook around island (5)
I believe the answer is:
chief
'head' is the definition.
(I know that head can be written as chief)
'cook around island' is the wordplay.
'cook' becomes 'chef' (both can mean someone who cooks).
'around' means one lot of letters goes inside another.
'island' becomes 'i' (geographical abbreviation).
'chef' placed around 'i' is 'CHIEF'.
(Other definitions for chief that I've seen before include "Leader; most important" , "Tribal head" , "Ordinary type" , "Tribe leader" , "Person in charge, head" .)