Who are the supervisors of a faith

Depends what religion you are referencing, but usually its pastors or rabbis, or the allamah in islam.

When we talk about "Faith," we can refer to many religions, which is why depending on religion, your "faith supervisor" will depend. Normally this place is occupied by a person trained in the doctrine of religion and is responsible for establishing the correct procedures and it is also who judges the people who do not comply, we could say that a Supervisor of the Faith could be the shepherds, rabbis or priests