Short-duration GRBs with extended emission form a subclass of short GRBs, comprising about 15% of the short-duration sample. Afterglow detections of short GRBs are also rare (about 30%) due to their smaller luminosity. We present a multi-band data set of the short burst with extended emission GRB 150424A, comprising of GROND observations, complemented with data from Swift/UVOT, Swift/XRT, HST, Keck/LRIS and data points from the literature. The GRB 150424A afterglow shows an extended plateau phase, lasting about 8hrs. The analysis of this unique GRB afterglow might shed light on the understanding of afterglow plateau emission, the nature of which is still under debate. We present a phenomenological analysis by applying fireball closure relations, and interpret the findings in the context of the fireball model. We discuss the plausibility of a magnetar as a central engine, being responsible for additional and prolonged energy injection into the fireball. We find convincing evidence for energy injection into the afterglow of GRB 150424A. We find that a magnetar spin down as source for a prolonged energy injection requires that at least 4% of the spin-down energy is converted to radiation.