We are not told whether or not there is a relationship between the high priest and the king, Gilead. It would not be surprising, as it was not unusual in the ancient world to have a king apportion important positions to his own kin. Given the intra-kin-group murders that have been part of Jaredite history, it is certainly plausible.
However, the high priest does not sit long on the throne. There was one who was part of the conspiracy who wanted the throne, and he kills the high priest to get it. We now begin the story of Lib, and man whose name appears in the Jaredite king-list from almost four hundred years earlier.