Give the go ahead to a mug (11)
I believe the answer is:
countenance
I believe this clue is a double definition.
'give the go ahead to' is the first definition.
(both can mean to approve or allow)
'a mug' is the second definition.
(both can mean a face)
(Other definitions for countenance that I've seen before include "Favour" , "features" , "Approve of - human face" , "brook" , "Accept as possible; face" .)