graocracy
A government led by old women or old men.
archaic, rare
And such, we are fully persuaded, will be the sentiments of every ancient dame in the British empire, who shall read the account we shall now give of the vaunted bonne Societé, under Madame de Genlis's admired and lamented graocracy.
Where it comes from
From Ancient Greek γραῦς (graûs, “old woman”) + -ocracy.
Adapted from the Wiktionary entry graocracy (CC BY-SA 4.0).