Emperor resigns over housing blunder (5)
I believe the answer is:
error
'blunder' is the definition.
(I've seen this in another clue)
'emperor resigns over housing' is the wordplay.
'housing' says the answer is hidden in the clue (part of the clue houses the answer).
'over' is a reversal indicator.
'rorre' can be found hidden inside 'emperor resigns'.
'rorre' backwards is 'ERROR'.
(Other definitions for error that I've seen before include "Fallacy, mistake" , "Howler" , "Slip, mistake" , "Boo-boo" , "Blunder or mistake" .)