Face matter better with husband absent (11)
I believe the answer is:
countenance
'face' is the definition.
(countenance is a kind of face)
'matter better with husband absent' is the wordplay.
I cannot really see how this works, but
'matter' could be 'te' (Te is an example) and 'te' is found within the answer.
This may be the basis of clue (or it may be nonsense).
(Other definitions for countenance that I've seen before include "Visage; accept as possible" , "Tolerate - face" , "appearance" , "Approve of - human face" , "brook" .)