Grazing animal's heading off for grass (3)
I believe the answer is:
oat
'grass' is the definition.
(I've seen this in other clues)
'grazing animal's heading off' is the wordplay.
'grazing animal' becomes 'goat' (goats graze).
'heading off' means to remove the first letter.
'goat' with its first letter removed is 'OAT'.
'for' is the link.
(Other definitions for oat that I've seen before include "Cereal (singular)" , "Cereal plant" , "Basis of porridge" , "Cereal grass" , "Food grain" .)