We theoretically investigate the subradiance dynamics in a nonreciprocal chiral-coupled atomic chain, in which infinite-range dipole-dipole interaction emerges in the dissipation. We find that super- and subradiance are both present in the dissipation process following single photon excitation, and the decay dynamics shows burst emissions from uniform initial excitations, which reflects the influence of atomic ordering on the propagation of light-induced atom-atom correlations. By tuning the nonreciprocal couplings in the chiral-coupled atomic system, we show that the subradiance dynamics can be greatly modified. We further study the effect of atomic local disorder, and find occurrence of plateaus on the decay curve dependent on the defect locations, as well as persistent localized excitations induced by disorders. We also discuss the effect of imperfections of systems on the subradiance dynamics. Our results show rich opportunities in the chiral-coupled system toward photon storage and routing.