Their music leaves American vagrants breathless! (5)
I believe the answer is:
oboes
'american vagrants breathless' is the definition.
I can't tell whether this definition defines the answer.
'their music' is the wordplay.
I cannot quite understand how this works, but
'music' could be 'e' and 'e' is present in the answer.
The remaining letters 'obos' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'leaves' acts as a link.
Can you help me to learn more?
(Other definitions for oboes that I've seen before include "They're instrumental" , "Woodwind instruments" , "Reed instruments" , "Wind instruments" , "noted producers" .)