Is inheriting kingship forbidden?

If by 'inheriting the kingship' you mean that the ruler entrusts governance to his son or one of his relatives, then this may be permissible if he gives it to someone who is fit to rule and meets the Sharia conditions. It is not permissible if he gives it to someone who is not fit, because the fundamental purpose of governance is to manage worldly affairs through religion and to safeguard the religious and worldly interests of Muslims.