Might sound like Roman from successful period (3)
I believe the answer is:
day
'successful period' is the definition.
(as in 'every dog has its day')
'might sound like roman from' is the wordplay.
'might sound like' indicates a 'sounds like' (homophone) clue.
'roman from' becomes 'de' ('from' in Latin).
'de' sounds like 'DAY'.
(Other definitions for day that I've seen before include "Unit of time" , "24-hour period" , "Lewis as poet" , "Twenty-four hours" , "24 hour period" .)