Woman given large bill? Why, might you say? (4)
I believe the answer is:
lady
'woman' is the definition.
(I know that lady is a type of woman)
'large bill? why might you say?' is the wordplay.
'large' becomes 'L' (eg in clothes sizes).
'bill?' becomes 'ad' (advertisement stuck on wall).
'might you say?' shows a homophone (sound like).
'why' sounds like 'y'.
'l'+'ad'+'y'='LADY'
'given' acts as a link.
(Other definitions for lady that I've seen before include "Female title" , "Female peer" , "Gentlewoman" , "See 2" , "See 19" .)