Is able to start or finish a dance (3)
I believe the answer is:
can
'is able to' is the definition.
(if you can do something you are able to do it)
'finish a dance' is the wordplay.
'finish' indicates taking half.
'a dance' becomes 'cancan' (cancan is a kind of dance).
'cancan' halved is 'CAN'.
'start or' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for can that I've seen before include "Tin; be able to" , "Preserve fruit" , "May" , "Airtight metal container" , "depth charge" .)