Rather small-minded about end of affair (6)
I believe the answer is:
pretty
'rather' is the definition.
('pretty' can be a synonym of 'rather')
'small-minded about end of affair' is the wordplay.
'small-minded' becomes 'petty' ('petty' can be a synonym of 'small-minded').
'about' means one lot of letters goes inside another.
'end of' indicates one should take the final letters.
The last letter of 'affair' is 'r'.
'petty' enclosing 'r' is 'PRETTY'.
(Other definitions for pretty that I've seen before include "Attractive in delicate way" , "sweet" , "Lovely" , "Attractive, beautiful" , "Attractive - quite" .)