"I Won't Dance" composer (4)
I believe the answer is:
'i won't dance composer' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for kern that I've seen before include "Jerome __ , Show Boat composer, d. 1945" , "Old soldier" , "See 14 Across" , "See 12" , "Popular composer" .)