Got better, looking embarrassed about European insurance (9)
I believe the answer is:
recovered
'got better' is the definition.
('recover' can be a synonym of 'get better')
'looking embarrassed about european insurance' is the wordplay.
'looking embarrassed' becomes 'red' (I've seen this before).
'about' means one lot of letters goes inside another.
'european' becomes 'E' (abbreviation e.g. EU).
'insurance' becomes 'cover' (I've seen this before).
'e'+'cover'='ecover'
'red' enclosing 'ecover' is 'RECOVERED'.
(Other definitions for recovered that I've seen before include "came round" , "Found after being lost" , "Found again - recuperated" , "Got better" , "Took back" .)