A new and distinct cultivar of Azalea plant named ‘RLH1-15P3’, characterized by its compact, upright to outwardly spreading and rounded plant habit freely basal branching habit dense and bushy appearance vigorous growth habit and rapid growth rate evergreen, persistent dark green-colored leaves that do not abscise during the winter freely flowering habit with remontant flowering during the spring, summer and autumn large, non-persistent single flowers that are white in color greenish white-colored central spots and speckles and excellent garden performance and temperature tolerance.