No, being a director does not by itself make a person an employee. A director is an officer of the company and becomes an employee only by entering into a separate employment contract with the company.
For example, a managing director working on an Employment Pass is also an employee of the company, whereas a nominee director service provides a director with no employment relationship. Even if not an employee, a director still bears all duties and responsibilities under the Companies Act.
Lee Kim Alliance provides a company secretary service.
