Mythical creature ran cute organisation (7)
I believe the answer is:
centaur
'mythical creature' is the definition.
(centaur is a kind of mythical creature)
'ran cute organisation' is the wordplay.
'organisation' indicates an anagram.
'ran'+'cute'='rancute'
'rancute' is an anagram of 'CENTAUR'.
(Other definitions for centaur that I've seen before include "Half-man and half horse" , "Greek mythical creature" , "Mythical hybrid" , "Mythological creature" , "Mythological horse-man" .)