Made out to be a lady (4)
I believe the answer is:
dame
'a lady' is the definition.
('dame' can be a synonym of 'lady')
'made out' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'made' with letters rearranged gives 'DAME'.
'to be' acts as a link.
(Other definitions for dame that I've seen before include "Panto cross-dresser" , "Broad" , "Female equivalent of British sir" , "Title of great actresses" , "Lady's title" .)