Reusing butter used as a frying agent
In principle you could proceed as you suggested. However, a few small tweaks may improve the overall results.
1. Straining the remaining fat.

Small particles of whatever is floating in the fat (either added on purpose or just pieces of water food you were frying) will be tasty in the first round of frying, but probably just burn and turn bitter in subsequent rounds. Just remember how most recipes will warn against letting garlic fry too much lest it becomes bitter. Burned herbs aren’t pleasurable either.
And fat will extract flavors, so what is a nicely aromatic mix in the beginning may become overpowering after a few days of storage if you leave the crushed garlic clove, peppercorns or twig of rosemary in the butter.

2. Letting the fat cool down or at least float to the top in a jar or jug and then draining off liquid at the bottom / skimming off just the fat.

Depending on your cooking process and ingredients, your food may have exuded quite a bit of liquid. If you try to fry in a fat + liquid mix, you will inevitably get a lot of splattering.
If you cook off the liquid, you will get leftover particles, which tend to burn (see 1.) If you want to reuse the flavorful liquid, freeze it separately and add it to a sauce or finished dish.
Even without aromatics, the butter contains milk solids. When you heat the butter, they will solidify and can be removed (so that they don’t burn), so that you get clarified butter, which is very good for frying and quite stable in storage.

If you have sufficiently clarified and filtered your butter, storing it in the refrigerator instead of the freezer will suffice (unless you plan to keep it for months) and it will be easier to scoop out if you need just a small amount instead of the whole jar.