In order to sync displays over the network, or save to the disk for persistent displays across reloads. It is optional to register display serializers.

In a server plugin (Constructing Plugins), override registerDisplaySerializer, from here, you may register your own serializer.

@Override
public void registerDisplaySerializer(DisplaySerializerRegistry registry) {
	registry.register(MY_DISPLAY, new DisplaySerializer<MyDisplay>() {
		@Override
		public CompoundTag save(CompoundTag tag, MyDisplay display) {
			// Manipulate the nbt tag
			return tag;
		}

		@Override
		public MyDisplay read(CompoundTag tag) {
			// create the display
		}
	});
}