Songbird’s quiet after American’s finished (6)
I believe the answer is:
thrush
'songbird's' is the definition.
(thesaurus)
'quiet after american's finished' is the wordplay.
'quiet' becomes 'sh'.
'after' says to put letters next to each other.
'american's finished' becomes 'thru' (I can't explain this - if you can you should believe this answer much more).
'sh' put after 'thru' is 'THRUSH'.
(Other definitions for thrush that I've seen before include "sprue" , "Throstle" , "Bird that sings" , "Repetitive singer" , "Common songbird or throat infection" .)