Extract of 'Chicago', live rehearsal for musical (6)
I believe the answer is:
oliver
'musical' is the definition.
(I've seen this before)
'extract of chicago live rehearsal' is the wordplay.
'extract of' says the answer is hidden in the clue (I've seen this in other clues).
'OLIVER' is hidden in the letters of 'chicago live rehearsal'.
'for' is the link.
(Other definitions for oliver that I've seen before include "stage show" , "One taking pride in food" , "Hardy, maybe" , "Orphan recruited by criminal gang" , "Chef" .)