Arrogant coup leaders ousted. What a shame! (6)
I believe the answer is:
uppity
'arrogant' is the definition.
(I've seen this before)
'what a shame' is the wordplay.
'what' becomes 'up' (I can't explain this - if you can you should give a lot more credence to this answer).
'a shame' becomes 'pity' (synonyms).
'up'+'pity'='UPPITY'
'coup leaders ousted' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for uppity that I've seen before include "Self-important, arrogant" , "Informally presumptuous or arrogant" , "Pert; haughty" , "Needing to be slapped down?" , "Cheeky or presumptuous" .)