Record includes unknown composer (5)
I believe the answer is:
liszt
'composer' is the definition.
(Franz Liszt)
'record includes unknown' is the wordplay.
'record' becomes 'list' (I've seen this before).
'includes' is an insertion indicator.
'unknown' becomes 'z' (algebra).
'list' enclosing 'z' is 'LISZT'.
(Other definitions for liszt that I've seen before include "Hungarian composer,d. 1886" , "Franz -, Hung. pianist" , "Pianist, father of Cosima Wagner" , "Franz . . . . ., great Hungarian composer" , "Hungarian virtuoso composer" .)