Just as democracy means a system of government ruled by the dēmos, or the common people, gerontocracy refers to rule by the elderly. It was coined in the 19th century as a pejorative to describe the aged French parliament, but it can refer to any government whose leaders are of sufficiently advanced age.
While being long in the tooth does not automatically indicate diminished mental faculties, it's enough of a concern that many jobs—even those without the ability to deploy troops or launch nuclear weapons—have maximum age limits.
