Asylum seeker good to enter EU, free to travel (7)
I believe the answer is:
refugee
'asylum seeker' is the definition.
(I've seen this in another clue)
'good to enter eu free to travel' is the wordplay.
'good' becomes 'g' (abbreviation).
'to enter' means one lot of letters goes inside another.
'to travel' indicates anagramming the letters (I've seen 'travelled' mean this).
'eu'+'free'='eufree'
'eufree' with letters rearranged gives 'refuee'.
'g' placed inside 'refuee' is 'REFUGEE'.
(Other definitions for refugee that I've seen before include "One seeks shelter" , "one seeking shelter" , "Displaced person - fugitive" , "One fleeing troubles" , "Person who seeks sanctuary in another country" .)