Billy or Nanny (4)
I believe the answer is:
goat
This clue is a double definition.
'billy' is the first definition.
(thesaurus)
'nanny' is the second definition.
(nanny is a female goat)
(Other definitions for goat that I've seen before include "fool" , "Domesticated animal supplying milk, meat and wool" , "heavenly sign" , "Billy - nanny" , "Butting nanny, perhaps?" .)