Not completely Fair Lady (3)
I believe the answer is:
eve
'lady' is the definition.
(I've seen this before)
'not completely fair' is the wordplay.
'not completely' means to remove the last letter.
'fair' becomes 'even' (I've seen this before).
'even' with its last letter removed is 'EVE'.
(Other definitions for eve that I've seen before include "Previous day" , "comes before Jan. 1st" , "Girl" , "when it gets dark" , "'All About - - ' (Bette Davis film)" .)