Remit unlimited allowance to displaced person (8)
I believe the answer is:
emigrant
'displaced person' is the definition.
(thesaurus)
'remit unlimited allowance' is the wordplay.
'unlimited' indicates the central letters (remove the limits/outer letters).
'allowance' becomes 'grant' (both can mean money given to someone).
The centre of 'remit' is 'emi'.
'emi'+'grant'='EMIGRANT'
'to' acts as a link.
(Other definitions for emigrant that I've seen before include "Time Gran went abroad to settle" , "One who leaves to live in another country" , "One settling abroad" , "One leaving for another country" , "Write carelessly" .)