Crossword Genius

He has one Right successor (4)

Ross

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" .)

I've seen this clue in the Sydney Morning Herald.
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