by law a person whose right of inheritance is established, provided he or she outlives the ancestor, see also primogeniture.
in Great Britain, the eldest son of the sovereign, who succeeds to the Throne should he be alive at his parent's death, e.g. the Prince of Wales.
One who expects to be receive property from the estate of a family member, as long as she outlives that person.
An heir apparent is an heir who (short of a fundamental change in the situation) cannot be displaced from inheriting; the term is used in contrast to heir presumptive, the term for a conditional heir who is currently in line to inherit but could be displaced at any time in the future. Today these terms are most commonly used for heirs to hereditary titles, particularly monarchies. It is also used less formally to indicate someone who is the apparent 'anointed' successor to any position of power, e.g., a political or corporate leader.
For the usage of the term, see Heir Apparent