Aura surrounding American backing European state (9)
I believe the answer is:
emanation
'aura' is the definition.
(thesaurus)
'surrounding american backing european state' is the wordplay.
'surrounding' means one lot of letters goes inside another.
'american' becomes 'am' (abbreviation in some contexts).
'backing' shows that the letters should be reversed in order.
'european' becomes 'e' (abbreviation e.g. EU).
'state' becomes 'nation' ('nation' can be a synonym of 'state'**).
'am' back-to-front is 'ma'.
'e'+'nation'='enation'
'ma' placed into 'enation' is 'EMANATION'.
(Other definitions for emanation that I've seen before include "Something produced from a source" , "Something flowing out from a source" , "Pouring out" , "Something given off" , "discharge" .)