Long gentle simmering of stock-based sauces is important to bring impurities to the surface so that they can be skimmed off. At the end of cooking, the sauce should be almost translucent.
Remove the pan from the heat and add two to three tablespoons of cold stock or water from time to time during simmering to help bring the scum to the surface. Skim the surface of the sauce with a small metal ladle or spoon, removing as little as possible of the sauce itself (here velouté is shown).
Alternatively, set the pan half off the heat and skim off the impurities as they rise to the cooler side of the pan.