Cheerier islets improved part of England (14)
I believe the answer is:
leicestershire
'part of england' is the definition.
(I know that Leicestershire is part of England)
'cheerier islets improved' is the wordplay.
'improved' is an anagram indicator.
'cheerier'+'islets'='cheerierislets'
'cheerierislets' anagrammed gives 'LEICESTERSHIRE'.
(Other definitions for leicestershire that I've seen before include "somewhere in the Midlands" , "Cricket team" , "Source of cheese" , "Melton Mowbray county" , "English county" .)