Question

Which form of government, practiced in certain Greek city-states and in Persian empire describe a society ruled by a king or queen until his or her death at which point power passes on to a family member

Answer 1

It were be primarily a "monarchy" (usually an "absolute monarchy") in which power is passed on to a family member after the king or queen's death, since in such systems it is believed that the royal family in question is "appointed" by God.