Insured a customer, looking embarrassed (7)
I believe the answer is:
covered
'insured' is the definition.
('cover' can be a synonym of 'insure')
'a customer looking embarrassed' is the wordplay.
'a customer looking' becomes 'cove' (I can't justify this - if you can you should give a lot more credence to this answer).
'embarrassed' becomes 'red' (I've seen this before).
'cove'+'red'='COVERED'
Can you help me to learn more?
(Other definitions for covered that I've seen before include "Overlaid with something" , "Concealed; dealt with" , "Reported" , "Concealed; roofed over" , "Insured; enveloped" .)