gerontocracy
noun /ˌdʒerənˈtɒkrəsi/
  /ˌdʒerənˈtɑːkrəsi/
(plural gerontocracies)
 [countable, uncountable]- a state, society or group governed by old people; government by old peopleWord Originmid 19th cent.: from Greek gerōn, geront- ‘old man’ + -cracy.