Duke introducing American composer, a rich man (5)
I believe the answer is:
dives
'a rich man' is the definition.
(I've seen this before)
'duke introducing american composer' is the wordplay.
'duke' becomes 'd'.
'introducing' says to put letters next to each other.
'american composer' becomes 'ives' (I've seen this before).
'd'+'ives'='DIVES'
(Other definitions for dives that I've seen before include "Seedy clubs" , "Disreputable resorts" , "sort of nightclubs?" , "Nightclubs; rich man" , "Drops steeply" .)