Lovely being by island (4)
I believe the answer is:
peri
'lovely' is the definition.
The answer and definition can be both people as well as being singular nouns.
Perhaps you can see a link between them that I don't see?
'by island' is the wordplay.
'by' becomes 'per'.
'island' becomes 'i'.
'per'+'i'='PERI'
'being' is the link.
(Other definitions for peri that I've seen before include "Type of disembodied spirit or graceful young girl" , "Ripe as a kind of fairy" , "Fairy of Persian myth" , "Fairy (Pers. mythology)" , "Fairy queen" .)