Meat quickly offered, not half! (4)
I believe the answer is:
chop
'meat' is the definition.
(chop is a kind of meat)
'quickly offered not half' is the wordplay.
'quickly offered' becomes 'chop-chop' ('chop-chop' means very quickly).
'not half' means to take half the letters.
'chopchop' halved is 'CHOP'.
(Other definitions for chop that I've seen before include "Reduce drastically" , "Karate punch" , "Cut - a piece of meat" , "Hew" , "Thick slice of meat including rib" .)