“The gate of the inner court.” The east gate from the outside world to the outer courtyard of the Temple compound was always shut (Ezek. 44:1-2). However, the east gate of the inner courtyard was to be shut the six working days of the week but opened on the Sabbath and the new moon (the new moon started the new month in the Hebrew calendar). During the week people could enter the inner court through the north and south gates. Reasons for the east gate being open on the Sabbath and new moon likely include because on those days there would be a large number of worshipers in the Temple, and also to honor God who established the calendar.
“new moon.” The new moon, the beginning of the month, was celebrated with special sacrifices and offerings under the Law of Moses (Num. 28:11-15; 10:10), and it will be again in the Millennial Kingdom of Christ.