Keen on including composer's last piece of music (5)
I believe the answer is:
intro
'piece of music' is the definition.
(intro is a kind of piece of music)
'keen on including composer's last' is the wordplay.
'keen on' becomes 'into' (I've seen this before).
'including' indicates putting letters inside.
'last' says to take the final letters.
The last letter of 'composer' is 'r'.
'into' enclosing 'r' is 'INTRO'.
(Other definitions for intro that I've seen before include "Beginning (colloq.)" , "Musical opening" , "Opening bars to a piece of popular music" , "One starts" , "Opening instrumental passage of song" .)