Yellowing rose leaves with brown spots can have many causes, including nutrient deficiencies, pests, and fungal diseases:
Nutrient deficiencies
A lack of iron, magnesium, nitrogen, manganese, or zinc can cause leaves to turn yellow. Nitrogen deficiency can also cause older leaves to turn yellow and brown, soften, and fold in. If left untreated, the leaves may wilt and die.
Pests
Sucking insects like aphids, spider mites, and thrips can cause leaves to turn yellow and brown. Aphids can also cause stippling on the leaves and secrete a clear, sticky substance called honeydew. You can check for pests by turning the leaves over while tending to your garden.
Fungal diseases
Fungal diseases like black spot can cause leaves to turn yellow and develop dark brown spots. Black spot is a common and serious disease that can lead to defoliation. Black spot can cause rose leaves to turn yellow. It's a common fungal infection that manifests as irregular brown and black leaf spots surrounded by yellow halos. Eventually leaves succumb and drop off which can result in defoliation or plant loss if left untreated. Black spot can't be cured but it can be controlled. Remove and dispose of infected leaves including debris around the plant's base. Sanitize pruners between each cut and water at ground level. Water early in the day to allow for drying before nighttime temperatures drop.
For severe cases, apply a targeted fungicide to prevent spread.
Watering
Roses need, on average, 1 to 2 inches of water twice a week. Be prepared to adjust frequency during periods of hot, dry, and windy weather which cause soil moisture to evaporate quickly.