Military aide to call back shortly after flyer (6)
I believe the answer is:
batman
'military aide' is the definition.
(term for an army officer's servant)
'call back shortly after flyer' is the wordplay.
'call back shortly' becomes 'man' (I can't justify this - if you can you should give a lot more credence to this answer).
'after' is a charade indicator (letters next to each other).
'flyer' becomes 'bat' (something which flies).
'man' after 'bat' is 'BATMAN'.
'to' acts as a link.
(Other definitions for batman that I've seen before include "Comic strip character" , "Cartoon hero or officer's servant" , "Caped crusader of Gotham City, cartoon or cinema" , "Tender" , "cartoon character" .)