A little lady disheartened after insult (8)
I believe the answer is:
slightly
'a little' is the definition.
(thesaurus)
'lady disheartened after insult' is the wordplay.
'disheartened' says to hollow out the word (remove centre letters).
'after' means one lot of letters go next to another.
'insult' becomes 'slight' (I've seen this before**).
'lady' with its middle taken out is 'ly'.
'ly' put after 'slight' is 'SLIGHTLY'.
(Other definitions for slightly that I've seen before include "a tiny bit" , "Quite!" , "Mildly" , "To a small degree" , "Not very much" .)