A new rose plant designated ‘ZARsunorgdlt’ particularly distinguished by being a landscape (miniature) shrub rose having orange flowers with yellow on the lower surface of the flowers, a compact growth habit requiring little pruning, shows resistance to powdery mildew, rust, and black spot, grows vigorously on its own roots, and shown to be heat tolerant and cold hardy in trials, and hardy to USDA Zones 5 to 10, is disclosed.