Humphrey is making ordinary jazz style one to show off (8)
I believe the answer is:
braggart
'off' is the definition.
Both the definition and answer are adjectives. Perhaps there's a link between them I don't understand?
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for braggart that I've seen before include "Show-off" , "Big boaster" , "Big noter" , "Vain boaster" , "bigmouth" .)