Put up with person battering some fast food (7,7)
I believe the answer is:
quarter pounder
'some fast food' is the definition.
'put up with person battering' is the wordplay.
'put up with' becomes 'quarter'.
'person battering' becomes 'pounder'.
'quarter'+'pounder'='QUARTER POUNDER'
(Other definitions for quarter pounder that I've seen before include "Crown" , "dish?" , "hamburger?" .)