Monarch may be mad on the stage - what a tragedy! (4,4)
I believe the answer is:
king lear
'what a tragedy' is the definition.
(I've seen this before)
'monarch may be' is the wordplay.
'monarch' becomes 'king' (king is a kind of monarch).
'may be' becomes 'lear' (I can't justify this - if you can you should give a lot more credence to this answer).
'king'+'lear'='KING LEAR'
'mad on the stage' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for king lear that I've seen before include "Shakespeare play with storm scene" , "Shakespeare's foolish tragic monarch" , "Shakespearean tragedy" , "Shakespearian royal tragedy" , "One of Shakespeare's tragedies" .)