Go after young horse, ignoring a cow's noise (6)
I believe the answer is:
follow
'go after' is the definition.
(synonyms)
'young horse ignoring a cow's noise' is the wordplay.
'young horse' becomes 'foal' (I've seen this in another clue).
'ignoring' is a deletion indicator.
'cow's noise' becomes 'low' (low can mean a mooing sound).
'foal' with 'a' taken out is 'fol'.
'fol'+'low'='FOLLOW'
(Other definitions for follow that I've seen before include "Trail" , "Grasp" , "Go behind" , "Come next" , "Chase" .)