Piece of music has encore to follow (5)
I believe the answer is:
chase
'follow' is the definition.
('chase' can be a synonym of 'follow')
'piece of music has encore' is the wordplay.
'piece of' indicates the answer is hidden within the clue.
'CHASE' is hidden within 'music has encore'.
'to' is the link.
(Other definitions for chase that I've seen before include "Composed type accommodated in this" , "Pursuit" , "trail" , "Pursue, run after" , "Hurry" .)