Gerontocratic describes a government or other group that's run by old people. In ancient Greece, a gerontocratic council of elders was valued for its members' advanced age and wisdom.
If every member of a company's board of directors is over the age of 70, it's an organization with gerontocratic leadership. Similarly, if a country's ruling party consistently elects only leaders over the age of 75, its structure could be considered gerontocratic. A gerontocratic government may be referred to as a gerontocracy. Both gerontocratic and gerontocracy are derived from Greek roots geron, "old man," and kratia, "rule by."