Supporter in demonstration losing face (4)
I believe the answer is:
ally
'supporter' is the definition.
(I've seen this before)
'demonstration losing face' is the wordplay.
'demonstration' becomes 'rally'.
'losing face' means to remove the first letter.
'rally' with its initial letter removed is 'ALLY'.
'in' is the link.
(Other definitions for ally that I've seen before include "often helpful when cluing adverbs" , "Join forces with" , "State formally cooperating with another" , "Friendly nation" , "One on one's side" .)