The right to use public office to fulfill certain duties

Rights are typically understood as referring to political endowments to the individual. 

There is a cognate form of rights that refers to the economic duties of the collective. Those duties are, for example, to distribute the social excess equally among all members of society. 

Rights as duties is an interesting notion. Society has the right to care for the needy; it has the right to honor what was given to it by a higher authority; it has the right to select leaders who exercise wisdom and compassion. These are all society's rights as the fulfillment of duties the leadership have a right to exercise. 

Having the right to use the public office to fulfill certain duties is indeed something a society must afford to the leadership – as a right.