Despicable person, that woman? On the contrary (6)
I believe the answer is:
rather
'on the contrary' is the definition.
(thesaurus)
'despicable person that woman?' is the wordplay.
'despicable person' becomes 'rat' (I've seen this before).
'that woman?' becomes 'her' (**).
'rat'+'her'='RATHER'
(Other definitions for rather that I've seen before include "Slightly, more so than not (6" , "Fairly" , "Somewhat; more willingly" , "More precisely; instead of" , "Prefer" .)