Run into horse, as donkeys do (4)
I believe the answer is:
bray
'as donkeys do' is the definition.
(to bray is to make a donkey's noise)
'run into horse' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'into' means one lot of letters goes inside another.
'horse' becomes 'bay' (bay is a kind of horse).
'r' placed into 'bay' is 'BRAY'.
(Other definitions for bray that I've seen before include "Berkshire village with a long-serving, politically flexible 18th-century vicar" , "Donkey's cry" , "Sound like an ass" , "Noise of a donkey" , "Cry of an ass" .)