Unknown cuts record for composer (5)
I believe the answer is:
liszt
'for composer' is the definition.
(Franz Liszt)
'unknown cuts record' is the wordplay.
'unknown' becomes 'z' (algebra).
'cuts' indicates putting letters inside (some letters cut their way into other letters).
'record' becomes 'list' (list is a type of record).
'z' placed into 'list' is 'LISZT'.
(Other definitions for liszt that I've seen before include "Hungarian composer, d. 1886" , "with his partner, drunk?" , "Franz -, Hung. pianist" , "Pianist and composer Cockneys associate with Brahms" , "Hungarian composer,d. 1886" .)