Gift disheartened lady at once (9)
I believe the answer is:
presently
'at once' is the definition.
'gift disheartened lady' is the wordplay.
'gift' becomes 'present' (synonyms).
'disheartened' suggests removing the centre.
'lady' with its middle removed is 'ly'.
'present'+'ly'='PRESENTLY'
(Other definitions for presently that I've seen before include "At the moment" , "Before long" , "Soon, in a little while" , "In the near future" .)