Change horse's headgear after heading off (5)
I believe the answer is:
alter
'change' is the definition.
(synonyms)
'horse's headgear after heading off' is the wordplay.
'horse's headgear' becomes 'halter' (strap placed round a horse's head).
'after heading off' means to remove the first letter (the letter which heads the word is removed).
'halter' with its first letter taken off is 'ALTER'.
(Other definitions for alter that I've seen before include "Change, maybe later" , "Become different" , "Alert to change" , "Change, modify" , "reform" .)