Every so often I buy a bag of frozen boneless skinless chicken breasts, poach them, and then cut up the meat and freeze it for easy weekday meals. That’s the tip in a nutshell, but I’ll elaborate.
Once fully cold, the (small amount of) fat will float to the top and you can skim it off prior to using the broth or freezing it. I froze mine in a zip-top bag. I refrigerated mine overnight before skimming the fat and putting it in a bag. I also have stock in my freezer. Stock = made with chicken bones/carcass (and veggies/herbs), broth = made only with chicken/veggies/herbs.