I’ve seen a lot of cookbooks advocate the skimming of the fat from the stock. We prefer letting the fat settle in a layer on top of the stock as it cools. This way, the fat acts as a protective layer over the stock.
Bacteria need oxygen to grow, so by allowing the fat to rise to the top of the stock and settle we create a protective barrier between the stock and the oxygen in the air above. The stock will last a bit longer in the refrigerator if you keep the fat layer on it.
Just lift up the layer of fat and remove the stock when you want to use it. Every few days, bring the stock to a simmer for 10 minutes and let it cool, again with the fat forming a protective layer. Your stock can be stored in the refrigerator for up to a couple of weeks this way.