Looking embarrassed about vehicle having to be recovered (8)
I believe the answer is:
recouped
'recovered' is the definition.
('recoup' can be a synonym of 'recover')
'looking embarrassed about vehicle' is the wordplay.
'looking embarrassed' becomes 'red' (I've seen this before).
'about' indicates putting letters inside.
'vehicle' becomes 'coupe' (coupe is a kind of vehicle**).
'red' enclosing 'coupe' is 'RECOUPED'.
'having to be' is the link.
(Other definitions for recouped that I've seen before include "As compensation" , "Recovered, was reimbursed" .)