IPA: /ˈpeɪtriɑːrkeɪt/
KK: /ˈpeɪtriɑːrkeɪt/
The territory or authority ruled by a patriarch, which can also refer to the office or residence of a patriarch.
The patriarchate of the church was known for its influence in the community.
Patriarchate is formed from "patriarch" (from Greek "patriarchēs", meaning father or chief of a family) and "-ate" (a suffix used to form nouns indicating a state or condition). The word refers to the state or condition of being a patriarch, or the office and jurisdiction of a patriarch.
Think of a 'father' or 'chief' ('patriarch') leading a group, and the '-ate' indicating a state or condition — that's why patriarchate refers to the state of being a patriarch.