The iron mass in galaxy clusters is about 6 times larger than could have been produced by core-collapse SNe, assuming the stars in cluster galaxies formed with a standard IMF. Type-Ia SNe have been proposed as the alternative dominant iron source. We use our HST measurements of the cluster SN-Ia rate at high redshift to study the cluster iron enrichment scenario. The measurements can constrain the star-formation epoch and the SN-Ia progenitor models via the mean delay time between the formation of a stellar population and the explosion of some of its members as SNe-Ia. The low observed rate of cluster SNe-Ia at z ~ 1 pushes back the star-formation epoch in clusters to z > 2, and implies a short delay time. We also show a related analysis for high-z field SNe which implies, under some conditions, a long SN-Ia delay time. Thus, cluster enrichment by core-collapse SNe from a top-heavy IMF may remain the only viable option.