Emperor, one stumbling round capital in Rome (4)
I believe the answer is:
nero
'emperor' is the definition.
(Roman emperor)
'one stumbling round capital in rome' is the wordplay.
'stumbling' is an anagram indicator.
'round' means one lot of letters goes inside another.
'capital in' says to take the initial letters.
The first letter of 'rome' is 'r'.
'one' anagrammed gives 'neo'.
'neo' placed around 'r' is 'NERO'.
(Other definitions for nero that I've seen before include "Roman Emperor, 54-68 AD" , "Cruel Roman emperor" , "Roman emperor on the fiddle?" , "Famous fiddler" , "Emperor (who fiddled while Rome burned?) d. AD68" .)