A fine story that's pleasant (7)
I believe the answer is:
affable
'pleasant' is the definition.
(thesaurus)
'a fine story' is the wordplay.
'a fine' becomes 'af' (I've seen this in other clues).
'story' becomes 'fable' (fable is a kind of story).
'af'+'fable'='AFFABLE'
'that's' is the link.
(Other definitions for affable that I've seen before include "Obliging" , "Kindly" , "Pleasant and easygoing" , "Good-natured, sociable" , "Genial and cordial" .)