Depending on the type of settlement, the specific local arrangements, the specific time, etc.:

Either whoever the local warrior was who administered the swath of land the settlement belonged to, or the village council (the miyaza). Possibly also the priest of the local village shrine, who might act as a representant of the latter.

The villages which emerged during the later medieval period were essentially self-governed entities, with the male heads of the households of the upper-class population forming a village council, which gathered around the local shrine. The miyaza was divided into an old-men and a young-men group, with the former wielding decision-making powers in everyday administrative matters. The most important issues could be discussed by members of both groups. I am not aware of something like a “mayor,” or "village elder," so, a single person who dominated everyone else, having been a thing.

But of course, people being people, we can assume that, in practice, the opinions of the richest members of the community were a bit more important during discussions.