Victor losing face in private (5)
I believe the answer is:
inner
'private' is the definition.
(thesaurus)
'victor losing face' is the wordplay.
'victor' becomes 'winner' ('winner' can be a synonym of 'victor').
'losing face' means to remove the first letter.
'winner' with its initial letter taken away is 'INNER'.
'in' is the link.
(Other definitions for inner that I've seen before include "This part of city is at the old centre" , "Target next to bull" , "Target area" , "Nearer the middle" , "Very private room" .)