Personally, I would expect death to be treated like grave illness, but the effects depend on who has the power to say "this is the new king".

For example, the king has sole power to abdicate, and no one can force him to. He is extremely ill, and gives instructions that he relinquishes the crown and his son must now be king. An equivalent would be a dead king leaving in his testament the instruction that the crown is now his son's. He can then be resurrected, the same way he could be healed from a disease, but the crown stays where it is.
The ill king instead could say, "I give full power to my son and associate him to the duties of a king, but I am king, and he is not, and I can retract his powers." A dead king could leave in his testament "in case of death, proclaim X person regent, until I am resurrected".

Instead, it could be a parliament making these choices. It could be a religious figure. There could be other laws. There could be no law, and then it would be might makes right, or there would be powerful men meeting, more or less formally, to decide what to do.