Is an island river (4)
I believe the answer is:
isis
'river' is the definition.
(I've seen this before)
'is an island' is the wordplay.
'an island' becomes 'is'.
'is'+'is'='ISIS'
(Other definitions for isis that I've seen before include "Oxford river; goddess" , "Egyptian goddess and jihadist group" , "divinity" , "Repetitive Egyptian goddess" , "Egyptian goddess - Thames at Oxford" .)