amount paid to Director

If an appointment letter confirming the employment of the director with the company, the director will be eligible for the monthly salary and the company is liable to deduct TDS on the salary. But, the director may or may not be holding shares in the private company. It all comes down to the appointment letter stating the terms and conditions of the employment of the director.

Yes, the Director is holding shares in the company.

Moreover, if there is no appointment / agreement letter confirminng the employer-employee relationship, isn't there any other way to show this amount.

If fixed salary is paid, that will be subject to deduction of TDS u/s 92B, taking into consideration the annual taxable income.

If fixed consultancy fees are paid, that will be subject to deduction of TDS u/s 194J.

Even commission paid will be taxed u/s 194H.

mihir is correct 

But Take care the director should not draw any excess loan and the same should not attract provsions of secion 2(22) (e) deemd dividend