The woman for many a man (5)
I believe the answer is:
madam
'the woman' is the definition.
(madam is a kind of woman)
'many a man' is the wordplay.
'many' becomes 'm'.
'a man' becomes 'adam' (Adam is an example**).
'm'+'adam'='MADAM'
'for' is the link.
(Other definitions for madam that I've seen before include "Term of address to a woman" , "Titled lady" , "Conceited girl (colloq.)" , "precocious schoolgirl?" , "Leader of House of Congress" .)