Self-admirer obtained one in east of France (7)
I believe the answer is:
egotist
'self-admirer' is the definition.
(an egotist is self-obsessed)
'obtained one in east of france' is the wordplay.
'obtained' becomes 'got' ('get' can be a synonym of 'obtain').
'one' becomes 'I' (Roman numeral).
'in' means one lot of letters goes inside another.
'east of france' becomes 'est' ('east' in French).
'got'+'i'='goti'
'goti' going within 'est' is 'EGOTIST'.
(Other definitions for egotist that I've seen before include "Excessively conceited person" , "Person with inflated self-image" , "A self-absorbed and conceited person" , "Conceited and self-centred person" , "braggart" .)