Put up with Satchmo playing (7)
I believe the answer is:
stomach
'put up with' is the definition.
('stomach' can be a synonym of 'put up with')
'satchmo playing' is the wordplay.
'playing' is an anagram indicator.
'satchmo' anagrammed gives 'STOMACH'.
(Other definitions for stomach that I've seen before include "Bear - belly" , "Mac hosts his organ" , "Belly - tolerate!" , "Could Mac host this organ?" , "Corporation" .)