Your private licence follows you, not your address. If you pay the TV-licence, it will cover the use of television receivers for you, your spouse/partner and children living at home that are provided for. Your licence will also cover television receivers you have in your cabin, caravan or the like.
Any household members who provide for themselves, and have their own television in use, has to pay their own TV-licence.
The TV-licence must be paid, no matter what kind of television receiver you have, signal conditions or which TV-channels you choose to watch. This means that even if you use your television as a pc-screen, to play video games or in other ways use it, but not to watch television, you still have to pay the TV-licence.
The term television receiver includes TV, DVD with tuner, satellite receiver, decoder and similar equipment. In short, all devices that are able to receive or transmit television signals.
As of 01.01.2020, the license will cease. Read more here