Thin fabric? Not socially acceptable to stare (4)
I believe the answer is:
gaze
'stare' is the definition.
(gaze is a kind of stare)
'thin fabric? not socially acceptable' is the wordplay.
'thin fabric?' becomes 'gauze' (I've seen this before).
'not' indicates named letters should be taken away.
'socially acceptable' becomes 'u'.
'gauze' with 'u' removed is 'GAZE'.
'to' acts as a link.
(Other definitions for gaze that I've seen before include "A long fixed look" , "Look steadily" , "Look long and hard" , "Look vacantly" , "Intense stare" .)