Great activity that led to finished Verdi composition (9)
I believe the answer is:
overdrive
'great activity' is the definition.
(I know that overdrive is a type of great activity)
'finished verdi composition' is the wordplay.
'finished' becomes 'over' (over can mean finished or ended).
'composition' indicates anagramming the letters (letters arranged or composed in a different order).
'verdi' anagrammed gives 'drive'.
'over'+'drive'='OVERDRIVE'
'that led to' is the link.
(Other definitions for overdrive that I've seen before include "Find extra gear" , "Furious activity" , "State of excessive activity" , "High gear; excessive activity" , "Engine mechanism" .)