Directors who resign should always find a successor if at all possible and submit those names to the remaining board members. Prepare a written, dated, signed resignation letter that indicates the effective date of your resignation.The resignation of a North Carolina registered agent can be filed online via the North Carolina Secretary of State Online Business Services page. When stepping down from a director position, it's useful to offer a letter of resignation as formal documentation of your intent to leave. The companies act, 1956 does not contain any provisions governing resignation of director. Generally, the remaining board members appoint a replacement to serve out a resigning director's term. Resignation and Appointment.