Many an apparition is headless (4)
I believe the answer is:
host
'many' is the definition.
(thesaurus)
'an apparition is headless' is the wordplay.
'an apparition' becomes 'ghost' (ghost is a kind of apparition).
'is headless' means to remove the first letter.
'ghost' with its initial letter taken off is 'HOST'.
(Other definitions for host that I've seen before include "Large crowd" , "Compre" , "Party giver" , "Entertain" , "Myriad" .)