Embarrass a bishop with a demand to keep quiet (5)
I believe the answer is:
abash
'embarrass' is the definition.
('abash' can be a synonym of 'embarrass')
'a bishop with a demand to keep quiet' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'with' says to put letters next to each other.
'demand to keep quiet' becomes 'sh'.
'a'+'b'+'a'+'sh'='ABASH'
(Other definitions for abash that I've seen before include "Bring shame on" , "Cause to feel 4" , "Cause someone to feel embarrassed" , "Affront" , "Rattle" .)