Belief unacceptable round island (6)
I believe the answer is:
notion
'belief' is the definition.
('notion' can be a synonym of 'belief')
'unacceptable round island' is the wordplay.
'unacceptable' becomes 'noton' (I've seen this before).
'round' indicates putting letters inside.
'island' becomes 'i'.
'noton' enclosing 'i' is 'NOTION'.
(Other definitions for notion that I've seen before include "Idea, belief" , "Concept, belief" , "Vague or fanciful idea" , "Whim or fancy" , "Idea or whim" .)