Cold girl -- one starts to beguile all lovers as man-eater (8)
I believe the answer is:
cannibal
'man-eater' is the definition.
('cannibal' can be a synonym of 'man-eater')
'cold girl one starts to beguile all lovers' is the wordplay.
'cold' becomes 'c' (eg on taps).
'girl' becomes 'anni' (**).
'one starts to' suggests taking the first letters.
The first letters of 'beguile all lovers' is 'bal'.
'c'+'anni'+'bal'='CANNIBAL'
'as' is the link.
(Other definitions for cannibal that I've seen before include "Person who has someone for dinner?" , "Eater of one's own kind" , "Fellow consumer" , "One eating own species" , "One who eats its own species" .)