The rendered chicken fat (aka schmaltz) breaks down a bit during the stock-making process and can be a bit less useful thaan that rendered as is typical, over low heat. Still, it's better than fat subjected to high temps (like renderings from roast chicken); it need only be further clarified should you want to cook in it. (Re-render gently then strain using a fine strainer, twice if necessary.)
For use as is toast and biscuits are good ideas. It is also used to flavor a variety of dumplings and fillings, like those for knish, both found in Jewish cuisine. You can finesse this sort of idea by adding it to mashed potatoes, replacing all or some of the butter, or mix it with bread crumbs and herbs for stuffing roasted onions.
If you have chicken skin on hand, chop some up and fry in the strained schmaltz. Delicious.