Count him among the jazz greats (5)
I believe the answer is:
basie
'count' is the definition.
(I've seen this before)
'him among the jazz greats' is the wordplay.
I cannot really see how this works, but
'him' could be 'si' and 'si' is present in the answer.
This may be the basis of clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for basie that I've seen before include "Count ___ , US jazz pianist, d. 1984" , "Jazz musician" , "jazz great" , "Band leader" , "Bandleader Count" .)