Rib woman when Guardian has leader cut (3)
I believe the answer is:
eve
'rib woman' is the definition.
(Eve was made from Adam's rib)
'guardian has leader cut' is the wordplay.
'guardian has' becomes 'we've' ('we have', referring to the setter's newspaper).
'leader cut' means to remove the first letter.
'weve' with its first letter removed is 'EVE'.
'when' acts as a link.
(Other definitions for eve that I've seen before include "See 27" , "First mate" , "Mother of Abel" , "Day before; first woman" , "'All About - - ' (Bette Davis film)" .)