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That gate - The eastern gate of the inner court. See (Ezekiel 46:2).

And when the prince shall enter, he shall go in by the way of
the porch of that gate (See Gill on Ezekiel 46:2…

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