The prince will enter the entry room of the gateway from the outside. Then he will stand by the gatepost while the priest offers his burnt offering and peace offering. He will bow down in worship inside the gateway passage and then go back out the way he came. The gateway will not be closed until evening.
4
In the time of Solomon, priest, king, and people each took his due part in the temple-service. Of the later kings some forsook Yahweh for false god…

Stand by the post of the gate.— The prince is to enter the sanctuary by the east gate of the outer court, pass through th…

And the prince shall enter by the way of the porch of that gate
without
That is, by the…

The ordinances of worship for the prince and for the people are described here, along with the gifts the prince may bestow on his sons and servants…
Albert Barnes
AlbertBarnes