Eagle inhabiting Alderney (4)
I believe the answer is:
erne
'eagle' is the definition.
(erne is a kind of eagle)
'inhabiting alderney' is the wordplay.
'inhabiting' indicates the answer is hidden within the clue.
'ERNE' is hidden within 'alderney'.
(Other definitions for erne that I've seen before include "Great lake in Fermanagh with lots of islands" , "Lough of the North" , "European sea eagle" , "Light (a flame)" , "one that catches fish?" .)