Little space, I acknowledge, for asylum seeker? (8)
I believe the answer is:
emigrant
'asylum seeker?' is the definition.
'little space i acknowledge' is the wordplay.
'little space' becomes 'em' (typographical space as wide as an 'm').
'acknowledge' becomes 'grant'.
'em'+'i'+'grant'='EMIGRANT'
'for' acts as a link.
(Other definitions for emigrant that I've seen before include "Write carelessly" , "Time Gran went abroad to settle" , "one on the way out?" , "One leaving for another country" , "One who leaves to live in another country" .)