Emperor's refusal to admit head of state (4)
I believe the answer is:
nero
'emperor's' is the definition.
(Roman emperor)
'refusal to admit head of state' is the wordplay.
'refusal' becomes 'no'.
'to admit' means one lot of letters goes inside another.
'head of state' becomes 'er' (abbreviation for Elizabeth Regina).
'no' placed around 'er' is 'NERO'.
(Other definitions for nero that I've seen before include "Roman tyrant" , "Barbarous Roman emperor" , "Emperor (who fiddled while Rome burned?) d. AD68" , "Wicked fiddler" , "Roman Emperor notorious for vice and luxury" .)