Do ordinary taxpayers need to sign any agreement with accountants when hiring part-time accountants?

You can sign or not, depending on the wishes of both parties.

General taxpayers refer to enterprises and business units whose annual sales of value-added tax (hereinafter referred to as annual taxable sales, including all taxable sales in a calendar year) exceed the standard of small-scale taxpayers stipulated by the Ministry of Finance. The characteristic of ordinary taxpayers is that the input tax of value-added tax can be deducted from the output tax.