Nero sloshed with ale demands woman (7)
I believe the answer is:
eleanor
'woman' is the definition.
'nero sloshed with ale' is the wordplay.
'sloshed with' indicates anagramming the letters.
'nero' anagrammed with 'ale' makes 'ELEANOR'.
'demands' is the link.
(Other definitions for eleanor that I've seen before include "Wife of F. D. Roosevelt" , "woman" , "English queen" , "Miss Rigby" , "Near Leo (anag) - girl's name" .)