Looking embarrassed in company -- that's the belief (5)
I believe the answer is:
credo
'the belief' is the definition.
(credo is a kind of belief)
'looking embarrassed in company' is the wordplay.
'looking embarrassed' becomes 'red' (I've seen this before).
'in' means one lot of letters goes inside another.
'company' becomes 'co' (abbreviation).
'red' put within 'co' is 'CREDO'.
'that's' is the link.
(Other definitions for credo that I've seen before include "One's system of beliefs" , "Guiding principles" , "set of ideas" , "Dogma" , "Part of the service" .)