Close to gracious twin lady, disheartened with craft (5)
I believe the answer is:
slyly
'with craft' is the definition.
(I've seen this in another clue)
'close to gracious twin lady disheartened' is the wordplay.
'close to' indicates one should take the final letters (the close of something is the end).
'twin' says to double the letters.
'disheartened' suggests removing the centre (the middle or heart is removed).
'lady' with its middle removed is 'ly'.
The final letter of 'gracious' is 's'.
'ly' duplicated is 'lyly'.
's'+'lyly'='SLYLY'
(Other definitions for slyly that I've seen before include "In a stealthy and secret way" , "In a cunning manner" , "in underhand way" , "Craftily, cunningly" .)