The correct answer is traditional.
Traditional authority refers to when an authority figure or the way in which authority operates is set in a traditional manner. This means that the "tried and tested" approach and conventions which have been used in the past are adopted when it comes authority and beliefs about how authority should be exercised. In this instance, where King Tut inherited the throne in Egypt from his father because cultural norms dictated that a king's son succeed him, represents a traditional authority.
