A few tips on how to look after and store your nuts…
Store nuts in the freezer. It will prolong their life as they can go rancid rather quickly.
Containers that have air-tight seals like glass jars and plastic containers should be used when storing nuts. This ensures your stored nuts will maintain the proper moisture level.
If you do have to store at room temperature, make sure to choose a dark space without direct heat. If sealed correctly, nuts can maintain freshness for up to 3 months in this short term storage.
The shelf life of nuts depends on three key factors: storage conditions, shelled or unshelled, and whether or not the package is opened. A good rule of thumb is to think of nuts as produce rather than a packaged good.
Chestnuts are not as shelf-stable as other nut varieties and must be handled differently. They do not need to be dried, but they do need to be frozen.
Source: Truly Good Foods Real Simple The Spruce Eats
