the world > relative properties > order > agreement, harmony, or congruity > suitability or appropriateness > [noun] > that which is suitable or appropriate > the appropriate person (3)
With the. Also with capital initial. Chiefly in predicative use: the man referred to previously; the man most suitable for some office, task, etc…
old who: the right man. Obsolete.
With possessive. the person who can fulfil one's requirements; the person whom one is seeking out or pursuing. See also sense 7a.