Put out about old woman, one moving abroad (8)
I believe the answer is:
emigrant
'one moving abroad' is the definition.
'put out about old woman' is the wordplay.
'put out' becomes 'emit' (I've seen this before).
'about' is an insertion indicator.
'old woman' becomes 'gran' (I've seen this in other clues).
'emit' going around 'gran' is 'EMIGRANT'.
(Other definitions for emigrant that I've seen before include "I've left home for good" , "One going abroad permanently" , "one on the way out?" , "Write carelessly" , "One who leaves to live in another country" .)