One may want political asylum before capturing Russian fighter (6)
I believe the answer is:
emigre
'one may want political asylum' is the definition.
(someone emigrating)
'before capturing russian fighter' is the wordplay.
'before' becomes 'ere' (poetic term for 'before').
'capturing' indicates putting letters inside.
'russian fighter' becomes 'MiG' (Russian fighter plane manufacturer).
'ere' enclosing 'mig' is 'EMIGRE'.
(Other definitions for emigre that I've seen before include "One gone abroad for political reasons" , "A political exile from regime" , "Person moving abroad" , "settler" , "One living abroad for political reasons" .)