One goes around circling King-Emperor (4)
I believe the answer is:
nero
'emperor' is the definition.
(Roman emperor)
'one goes around circling king' is the wordplay.
'goes around' is an anagram indicator.
'circling' means one lot of letters goes inside another (circling can mean going around or containing).
'king' becomes 'r' (r is abbreviation for rex).
'one' with letters rearranged gives 'neo'.
'neo' going around 'r' is 'NERO'.
(Other definitions for nero that I've seen before include "Emperor who played the fiddle" , "Roman emperor who fiddled while Rome burned" , "Ancient Roman emperor" , "Cruel Roman emperor" , "Roman emperor, d. AD68" .)