Grab when eating horse meat slice (4)
I believe the answer is:
chop
'meat slice' is the definition.
'grab when eating horse' is the wordplay.
'grab' becomes 'cop' (both can mean to obtain).
'when eating' indicates putting letters inside.
'horse' becomes 'H' (synonyms).
'cop' going around 'h' is 'CHOP'.
(Other definitions for chop that I've seen before include "Cut of meat; hack" , "Karate blow" , "Thick slice of meat, often with rib" , "Small cut of meat" , "Cutting blow" .)