There’s Alhaitham and Nahida. And Cyno’s basically the head of police while Tighnari is the lead forest watcher

Jean and Venti. Though Varka’s the official grandmaster, Jean is functionally the head of government till Mondstat is expanded and Varka comes back

Zhongli and the Qixing, although the Qixing are several individuals

Raiden and The Tri Commission. People keep thinking of Yae. No. Yae is not head of government. Or even a government official. The Tri Commission are the government. And iirc the Grand Narukami Shrine is under the jurisdiction and care of The Yashiro Commission and the Kamisato Clan. I think Raiden herself says the Yashiro commission is in charge of taking care of it’s roots?

Really, part of Yae’s political and social status is from her personal connection to Ei

The Tsaritsa and Pierro. Though I dunno if Pierro or the Harbingers are technically part of the governing body or if people just have to listen to them or else they get killed lol

There’s plenty of examples of the Archon being of different gender to their governing officials

People just keep misunderstanding it seems, just because of who’s close to the archon/or who gets the spotlight when interacting with the Traveller during Archon quests