The department may issue a certificate of convenience to the executor, executrix, administrator or administratrix of the estate of a deceased holder of validly outstanding special plates and license issued under this chapter, or if no executor, executrix, administrator or administratrix had been appointed, and until a certified copy of an order making such appointment is filed with the department, to the widow or other heir otherwise entitled to conduct the business of the deceased, permitting such person to exercise the privileges granted by such special plates and license for a period of one year from and after the date of death, pending, but not later than, disposal of the business and qualifications of the vendor of the business or such surviving widow or heir for such special plates and license under the provisions of this chapter. The department may restrict or condition the license and special plates and attach to the exercise of the privileges thereunder such terms and conditions as in its judgment the protection of the public requires.