Cheek or part of mouth (3)
I believe the answer is:
lip
I believe this is a triple definition!
'cheek' is the first definition.
(both can mean insolence or rudeness)
'or' is a link.
'part' is the second definition.
(lip is a kind of part)
'of' acts as a link.
'mouth' is the third definition.
(synonyms)
(Other definitions for lip that I've seen before include "Sauce" , "Brim" , "Edge of mouth" , "Oral impudence?" , "Edge; impudent talk" .)