Special guidelines are set for a leader who wishes to bring a voluntary offering during a regular workday. These rules highlight the deep respect given to the prince while drawing a clear practical line between days of rest and days of labor in the Temple.
Commentators agree that these instructions apply strictly to the six ordinary days of the week, as the procedures for the Sabbath and the new moon were already established. Ordinarily, during the workweek, the eastern gate of the inner courtyard remains firmly shut. However, when the prince arrives to present his offering, the gatekeepers open this specific gate just for him. This act is designed to show him special honor [רד״ק, מלבי״ם]. By opening the gate, the prince's ordinary weekday offering is elevated, taking on the same majesty and splendor as an offering brought on a day of rest [רד״ק, אברבנאל].
The actual process of the sacrifice is identical to the routine followed on holy days. The same standard applies to the new moon, though it is not explicitly mentioned here simply to keep the instructions brief [מצודת דוד]. During the service, the prince does not step inside the Sanctuary itself. Instead, he stands within the space of the gateway, looking toward the altar. The priests carry out the physical work of the sacrifice on his behalf while he stands there, and upon completion, he bows in worship [רש״י, מצודת דוד, שטיינזלץ].
The core difference between a weekday and a holy day becomes clear at the very end of the service. On the Sabbath and the new moon, the eastern gate remains open until the evening. Because the general public is free from their daily labor, large numbers of people arrive to bow before God. On a regular weekday, however, the people are busy with their normal work and do not gather at the Temple. Therefore, the moment the prince finishes his worship and departs, the gatekeeper immediately closes the gate behind him [רש״י, רד״ק, אברבנאל].