There are three essential policies that your council should have: a complaints policy, a discipline policy and a grievance policy. Each should have clearly defined procedures for handling complaints against the council and against council staff. Without them, your council is already at a disadvantage if or when a complaint is made, whether a valid complaint or not. Those documents should be your starting point.
The Clerk is an employee of the council and you have referred to "other councillors" when referring to complaints about the clerk. You, the Council, are the clerk's employer and must act as such. The Mayor alone has no jurisdiction unless or until you have followed the disciplinary/complaints procedure.
If your complaint is about the actions of the clerk/council in a financial matter, then you can and should raise this with your internal and external auditor.