Hindu queen administered island (4)
I believe the answer is:
rani
'hindu queen' is the definition.
(I've seen this before)
'administered island' is the wordplay.
'administered' becomes 'ran' (I've seen this before).
'island' becomes 'i'.
'ran'+'i'='RANI'
(Other definitions for rani that I've seen before include "Wife of a rajah" , "Raja's queen" , "Wife of a raja" , "Member of royal family" , "Rajah's wife from Iran" .)