Not an expert, by I'd guess powdery mildew

It also looks to me like some kind of mildew.
spray it with 20/80 milk/water mixture. it is not going to hurt it , if did not help.

BTW, is it in shade and moist environment ?

Thanks seysonn. The plants are in a sunny area and they get pretty good drainage. Not moist and not dry.
I'll give the milk/water spray a shot this weekend.

You say you haven't fertilised 'yet'. Rosemary doesn't need fertiliser at all. It just promotes sappy weak growth which will be prey to diseases and pests. Moist soil won't hurt it provided there is reasonable drainage. It grows happily under our grey skies and downpours and I have never seen powdery mildew on it here. It seems to be worst when rosemary is kept indoors over the winter. Some powdery mildews are actually a sign of water stress so make sure your rosemary has enough. It goes against one's tendency to view mildew as a symptom of damp but I would give the plant a few thorough showers from the hose too.

Leafhopper I have a microscope and found them on my rosemary and lavender. https://ag.umass.edu/greenhouse-floriculture/photos/leafhopper-damage-to-rosemary