Heir
Part of speech: noun
Definition: Someone who inherits, or is designated to inherit, the property of another. One who inherits, or has been designated to inherit, a hereditary title or office. A successor in a role, representing continuity with the predecessor.
Example sentence: Anytime you have a reelection campaign against an incumbent president and you're the party out of power - on the one hand it's wide open because there's not an heir apparent - but people are also gauging how strong is that incumbent president and what are my chances.
Successor
Part of speech: noun
Definition: A person or thing that immediately follows another in holding an office or title.The next heir in order or succession.A person who inherits a title or officeThe integer immediately following another
Example sentence: A woman finds the natural lay of the land almost unconsciously; and not feeling it incumbent on her to be guide and philosopher to any successor, she takes little pains to mark the route by which she is making her ascent.