Rapid with notes, I’m accepted by a military association (7)
I believe the answer is:
animato
'rapid with notes' is the definition.
(musical term)
'i'm accepted by a military association' is the wordplay.
'accepted by' means one lot of letters goes inside another.
'military association' becomes 'NATO' (North Atlantic Treaty Organisation).
'a'+'nato'='anato'
'im' inserted within 'anato' is 'ANIMATO'.
(Other definitions for animato that I've seen before include "Fire" , "Performed musically in lively manner" , "Orchestra's lively" .)