He has one Right successor (4)
I believe the answer is:
heir
'successor' is the definition.
(synonyms)
'he has one right' is the wordplay.
'has' is a charade indicator (letters next to each other).
'one' becomes 'i' (Roman numeral).
'right' becomes 'r' (common abbreviation).
'he'+'i'+'r'='HEIR'
(Other definitions for heir that I've seen before include "Natural successor" , "One expected to succeed?" , "Beneficiary, inheritor" , "Person who inherits" , "One who will succeed to title" .)