Finished piece of music out of time and late (7)
I believe the answer is:
overdue
'late' is the definition.
('overdue' can be similar in meaning to 'late')
'finished piece of music out' is the wordplay.
'finished' becomes 'over' ('over' can be similar in meaning to 'finished').
'piece of music' becomes 'duet' (duet is a kind of piece of music).
'out' means to remove the last letter.
'duet' with its last letter removed is 'due'.
'over'+'due'='OVERDUE'
'of time and' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for overdue that I've seen before include "unsettled" , "Not paid by the agreed time, late" , "Later than the appointed time, as for bill payment" , "Not paid by the appropriate time" , "Beyond the expected time" .)