Jazz trumpeter with stomach upset (7)

I believe the answer is:

satchmo

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'jazz trumpeter' is the definition.
'satchmo' can be an answer for 'trumpeter' (I've seen this before). I'm not sure about the 'jazz' bit.

'stomach upset' is the wordplay.
'upset' indicates anagramming the letters.
'stomach' anagrammed gives 'SATCHMO'.

'with' acts as a link.

Can you help me to learn more?

(Other definitions for satchmo that I've seen before include "Louis Armstrong's nickname" , "trumpeter" , "Louis Armstrong's byname" , "Name used by jazz player Louis Armstrong" , "Jazz musician" .)

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