Remove from moustache (4)
I believe the answer is:
oust
'remove' is the definition.
(I know that oust is a more specific form of the action remove)
'from moustache' is the wordplay.
'from' indicates the answer is hidden within the clue.
'OUST' is hidden within 'moustache'.
(Other definitions for oust that I've seen before include "responsible for expulsions" , "Throw out" , "Expel (from a place)" , "Force from office" , "Evict" .)