Cloak, better back on vampire (4)
I believe the answer is:
cape
'cloak' is the definition.
(I know that cape is a type of cloak)
'better back on vampire' is the wordplay.
'better' becomes 'cap' (both can mean to beat somebody else's attempt).
'back on' indicates one should take the final letters (the letter at the back).
The final letter of 'vampire' is 'e'.
'cap'+'e'='CAPE'
(Other definitions for cape that I've seen before include "Cloak; head" , "Wrap" , "Batman has one" , "Headland - garment" , "Wrath, say" .)