Compare half of horse's bit (6)
I believe the answer is:
equate
'compare' is the definition.
(I know that compare can be written as equate)
'half of horse's bit' is the wordplay.
'half of' means to take half the letters.
'horse's' becomes 'equid's'.
'bit' becomes 'ate' ('bite' can be similar in meaning to 'eat').
'equids' with half the letters taken is 'equ'.
'equ'+'ate'='EQUATE'
(Other definitions for equate that I've seen before include "Appear the same" , "Match" , "Regard (two things) as the same" , "Consider or describe as similar, equal, or analogous" , "Make or be similar" .)