Composer’s last letter found in register (5)
I believe the answer is:
liszt
'composer's' is the definition.
(Franz Liszt)
'last letter found in register' is the wordplay.
'last letter' becomes 'Z' (last letter of the alphabet).
'found in' means one lot of letters goes inside another.
'register' becomes 'list' (listing is a kind of registering).
'z' put inside 'list' is 'LISZT'.
(Other definitions for liszt that I've seen before include "half-drunk?" , "Franz -, Hung. pianist" , "Pianist and composer Cockneys associate with Brahms" , "Hungarian piano virtuoso, d. 1886" , "Hungarian composer, d. 1886" .)