Displaced persons, finally, receive an answer (8)
I believe the answer is:
response
'an answer' is the definition.
('response' can be a synonym of 'answer')
'displaced persons finally receive' is the wordplay.
'displaced' is an anagram indicator.
'finally' indicates one should take the final letters.
The last letter of 'receive' is 'e'.
'persons' is an anagram of 'respons'.
'respons'+'e'='RESPONSE'
(Other definitions for response that I've seen before include "'Answer, reply (8)'" , "Sees porn (anag) - answer" , "See porn (anag) -- answer" , "Preens so by way of answer" , "comeback" .)