If a whitish coating appears on the leaves of the privet in midsummer, it is usually powdery mildew. But you don't have to panic. The privet usually copes well with such a fungal attack on its own.

Powdery mildew on privet is usually harmless
Mildew on privet does not necessarily look pretty, but the fungal attack is not dangerous for a healthy privet. After the leaves are shed in winter, the problem usually resolves itself.
In the interest of the environment, it is better to avoid using sprays. Even home remedies can hardly be used with a privet hedge.
If necessary, cut off all affected shoots and dispose of them in the household waste.
tips
If the privet gets yellow leaves in summer, this is often due to an oversupply of nutrients. To prevent this discoloration, check if you need to fertilize at all. Rather use organic fertilizers such as a mulch layer to avoid over-fertilization.