European story, probed by Times, backing person living elsewhere (5)
I believe the answer is:
exile
'person living elsewhere' is the definition.
(someone who has been exiled)
'european story probed by times backing' is the wordplay.
'european' becomes 'e' (abbreviation e.g. EU).
'story' becomes 'lie' (story can mean a fabrication).
'probed by' indicates putting letters inside (I've seen this in other clues).
'times' becomes 'x' (multiplication sign).
'backing' shows that the letters should be reversed in order.
'e'+'lie'='elie'
'elie' going around 'x' is 'elixe'.
'elixe' back-to-front is 'EXILE'.
(Other definitions for exile that I've seen before include "Person absent from home or country" , "He is forced to live in another country" , "Outcast" , "One lives away from the home country" , "Eject from country" .)