Personnel in authority on island (8)
I believe the answer is:
manpower
'personnel' is the definition.
(manpower is a kind of personnel)
'authority on island' is the wordplay.
'authority' becomes 'power' (I've seen this in another clue).
'on' says to put letters next to each other.
'island' becomes 'man' (the Isle of Man is an example).
'power' put after 'man' is 'MANPOWER'.
'in' acts as a link.
(Other definitions for manpower that I've seen before include "Work force" , "Staff resources" , "Work effort" , "Workforce" , "People available for work" .)