Last character in register is a composer (5)
I believe the answer is:
liszt
'composer' is the definition.
(Franz Liszt)
'last character in register' is the wordplay.
'last character' becomes 'Z'.
'in' means one lot of letters goes inside another.
'register' becomes 'list' (listing is a kind of registering).
'z' inserted within 'list' is 'LISZT'.
'is a' acts as a link.
(Other definitions for liszt that I've seen before include "Hungarian piano virtuoso, d. 1886" , "Pianist, father of Cosima Wagner" , "Hungarian romantic composer" , "Pianist and composer (often associated with Brahms), d. 1886" , "Scorer" .)