Former partner playing tune in order to leave the stage (6)
I believe the answer is:
exeunt
'to leave the stage' is the definition.
(I've seen this before)
'former partner playing tune in' is the wordplay.
'former partner' becomes 'ex' ().
'playing' indicates an anagram.
'in' is an insertion indicator.
'tune' is an anagram of 'eunt'.
'ex' placed into 'eunt' is 'EXEUNT'.
'order' acts as a link.
This may not be correct. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for exeunt that I've seen before include "(Actors) leave stage" , "More than one exit?" , "Stage direction to a group of actors (Latin)" , "direction to get cast away" , "Stage direction (Latin, they go out)" .)