Alkaline zinc-air batteries (ZABs) have attracted interest in recent years for their high theoretical energy density and use of low-cost, abundant zinc metal as the anode. In order to overcome the activation energy barrier of the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), noble metals are commonly used. Within this work, transition metal-functionalized Poly(heptazine imide)s (PHIs) are studied as an alternative and more abundant electrocatalyst, as they offer the homogenous immobilization of metals within their ordered structure. Introducing Fe and Ni into the PHI network enables the formation of single and mixed transition metal PHIs, which show reduced overpotentials for ORR and OER. The formation of Ni single atoms even induces outstanding catalytic activity for the OER during charging of ZAB full cells with performance comparable to that of RuO$_2$. Furthermore, full cell tests show excellent stability over the course of 250 discharge-charge cycles, making it a promising system for sustainable energy storage. This work paves the way for the molecular design of a novel material class as an electrocatalyst for ZAB.