Given food — or a hat! (6)
I believe the answer is:
fedora
'hat' is the definition.
(fedora is a kind of hat)
'given food or a' is the wordplay.
'given food' becomes 'fed' (I've seen this before).
'fed'+'or'+'a'='FEDORA'
(Other definitions for fedora that I've seen before include "Felt hat dented lengthways" , "Cover for head" , "Style of hat" , "Brimmed hat with creased crown" , "Or fade away with man's soft felt hat" .)