Rule operating during parade at end of May (8)
I believe the answer is:
monarchy
'rule' is the definition.
(I've seen this before)
'operating during parade at end of may' is the wordplay.
'operating' becomes 'on' (I've seen this in other clues).
'during' is an insertion indicator.
'parade' becomes 'march' ('march' can be a synonym of 'parade').
'at end of' says to take the final letters.
The last letter of 'may' is 'y'.
'on' inserted into 'march' is 'monarch'.
'monarch'+'y'='MONARCHY'
(Other definitions for monarchy that I've seen before include "Kingship system" , "Rule by a king or queen" , "sort of government" , "kind of government" , "Kingdom - kingship" .)