As a vehicle owner, you must re-register your vehicle at a new address and apply for a new license plate if you move your place of residence to another municipality.

You may be exempt from re-registration (assignment of a new license plate) if you change vehicles within registration areas that use the same distinguishing codes. This applies only to the cities, counties, and regions of Göttingen, Hanover, Oldenburg, and Osnabrück. As things stand, there are no plans to extend this exemption from re-registration to other registration areas.

The requirement, as stipulated in the Vehicle Registration Ordinance, to re-register a vehicle when the vehicle owner moves to a different registration area was repealed as of January 1, 2015. Vehicle owners can now decide for themselves, when changing their place of residence within Germany, whether they wish to keep their current license plate or have a new one assigned. Please note that the obligation to report a change of residence to the relevant authority remains in effect, and an amendment to the Registration Certificate Part I (vehicle registration document) is still required.

You have a car.
Or you have a motorcycle.
And you now live in a different city or municipality.
Then you must re-register your vehicle.
This means:
You must get a new license plate.
However, you can also keep your old license plate.
In that case, you only need to register your place of residence.