Subject putting edge into disheartened theatre (5)
I believe the answer is:
theme
'subject' is the definition.
('theme' can be a synonym of 'subject')
'edge into disheartened theatre' is the wordplay.
'edge' becomes 'hem' (I've seen this before).
'into' means one lot of letters goes inside another.
'disheartened' suggests removing the centre.
'theatre' with its centre taken out is 'te'.
'hem' going inside 'te' is 'THEME'.
'putting' is the link.
(Other definitions for theme that I've seen before include "[(type of) PARK]" , "Short melody" , "Musical motif" , "matter for discussion" , "The main sound" .)