When you move, first complete the moving-out procedure at the city or ward office of your current address.
After that, within 14 days of moving to your new address, complete the moving-in procedure at the city or ward office of your new residence.
For these procedures, you will need your residence card, passport, and moving-out certificate.
You will also need to update the address for your National Health Insurance and My Number.
If you delay the procedures, you may face problems, such as not being able to visit a hospital.
Be sure to complete the procedures as soon as possible.

You can also read more about the detailed process at the link below.
Please check “1. Notification of Address (moving-in/out notification)” on the linked page.
Procedures at Municipal Offices | 留学＠JP ┃外国人進学・就職情報サイト