Head of council, stable occupant it's said (5)
I believe the answer is:
mayor
'head of council' is the definition.
'stable occupant it's said' is the wordplay.
'stable occupant' becomes 'mare'.
'it's said' indicates a 'sounds like' (homophone) clue.
'mare' sounds like 'MAYOR'.
(Other definitions for mayor that I've seen before include "Municipal head" , "Local government head" , "Civic leader" , "Johnson, say" , "Municipal official" .)