Enthusiastic about grabbing composer's final piece of music (5)
I believe the answer is:
intro
'piece of music' is the definition.
(intro is a kind of piece of music)
'enthusiastic about grabbing composer's final' is the wordplay.
'enthusiastic about' becomes 'into' (I've seen this before).
'grabbing' means one lot of letters goes inside another.
'final' suggests the final letters.
The final letter of 'composer' is 'r'.
'into' enclosing 'r' is 'INTRO'.
(Other definitions for intro that I've seen before include "First bars of a musical composition" , "Opening passage (abbr)" , "Opener" , "Song's opening" , "Nitro (anag.)" .)