Finale cut short before middle part: we want more! (6)
I believe the answer is:
encore
'we want more' is the definition.
(as in an audience calling 'encore! encore!')
'finale cut short before middle part' is the wordplay.
'finale' becomes 'end' (the end of a story or show).
'cut short' means to remove the last letter.
'before' says to put letters next to each other.
'middle part' becomes 'core' (core can mean the centre of something).
'end' with its last letter removed is 'en'.
'en'+'core'='ENCORE'
(Other definitions for encore that I've seen before include "(Call for) repeat performance" , "Call for additional item" , "Sing it again, please" , "Enthusiastic call" , "Request to sing it again" .)