Storing white tea cakes is simple, but there's a few things you'll have to keep in mind:
Temperature
Store the tea under normal room temperature. Do not store it in the fridge, because the environment will be too humid and the temperatures are too cold for proper aging. Also avoid direct sunlight as this will too much accelerate aging, negatively affecting the white tea leaf quality. A temperature between 20-30ºC (68 to 96 ºF) is considered to be ideal, though this also depends on the level of humidity.
Air ventilation
Make sure the storage area is well ventilated and there's no presence of strange smells that might get absorbed by the white tea cake. Kitchen cabinets are therefore a bad idea as your white tea cake will absorb the scent of food.
Humidity
The white tea cakes will need some humidity to age properly, but too much isn't good. That's why white cakes come with a paper wrapper, which will help absorb some excess humidity. Keeping the tea cake just in the wrapper in the cabinet will be sufficient in dry climate.
When the weather is very humid, it's better to keep the cake together with the wrapper temporarily in a sealable bag or airtight container. At the same time, it's good to sometimes unpack the white cake and let it air. Humidity around 70% is considered to be ideal.
Store together
If you've several cakes, it's better to store them together in a cabinet or box, dedicated for white tea cakes only. Don't store them with other tea types.