Same thing happened when I bought a cherry plant. I'm no expert, but I can tell you can't stop the infection from spreading. I collected the infected leaves throughout the summer until fall. In fall, when all the leaves have fallen, I applied a Chlorothalonil based fungicide. In spring, I again applied the same fungicide when the new leaves were emerging and also before the shock split. Follow the instructions on the label, but you may not need to apply so many times as I did. The most important thing to do is to collect all those infected leaves from the ground because that's the main way how the disease survives.

Agree with RD re. sanitation. Pick up infected leaves and throw them out with your trash. Do not compost.

Myclobutanil (one of the brand names is Immunox) is fungicide for cherry leave spot and apple cedar rust (if you have apples). Captan will work, too. Spray two weeks after petal fall (flowers drop their petals) and again in 10-14 days. It should work.

During a dormant season, you can spray copper. It is fungicide and bactericide and will help prevent several fungal/bacterial issues on fruit trees.

Thank you both for the help. So there is nothing I can apply to the leaves after petal fall to prevent the new growth from getting the fungus?

I think a sulfur based fungicide could work and would be safe, but I'm not sure. Others might know better. If you collect all the leaves and apply a fungicide before the leaves mature in spring (and maybe do some pruning if it's too bushy), the disease shouldn't come back. I see some shot holes on my leaves, so it might have gotten infected again. I'm not even sure if it's cherry leaf spot. It may be because I haven't prune it. But I can tell you that once I collected the leaves and applied the fungicide, I haven't had severe disease problems and the plant looks healthy.