Played by a folk musician in short run on old Greek stage (8)
I believe the answer is:
melodeon
'played by a folk musician' is the definition.
I can't judge whether this definition defines the answer.
'in short run on old greek stage' is the wordplay.
'in short' means to remove the last letter.
'run' becomes 'melt' (synonyms).
'on old greek stage' becomes 'odeon' (I can't justify this - if you can you should give a lot more credence to this answer).
'melt' with its last letter taken off is 'mel'.
'mel'+'odeon'='MELODEON'
Can you help me to learn more?
(Other definitions for melodeon that I've seen before include "music-maker" , "Kind of small reed organ" , "A kind of accordion" , "Small squeezebox" , "A small accordion" .)