Being worthy of respect? Conservative's looking embarrassed (4)
I believe the answer is:
cred
'being worthy of respect?' is the definition.
(eg street cred)
'conservative's looking embarrassed' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'looking embarrassed' becomes 'red' (someone may go red when embarrassed).
'c'+'red'='CRED'
(Other definitions for cred that I've seen before include "Street --, hipness" , "Little confidence" , "what goes a long way on the street" , "See 7" , "informal approval" .)