The design and development of high-performance electrochemical electrode materials are crucial for energy storage and conversion systems. This work reports a facile preparation of a self-supported Zn/Co-S@Ni(OH)2 array electrode in which a Zn/Co-S nanosheet is derived from a leaf-like zeolitic imidazolate framework (Zn/Co-ZIF-L). The core-shell structure provides multiple benefits such as enhanced electrical conductivity, an abundance of exposed active sites, and strong electronic interactions between Zn/Co-S and ultra-thin Ni(OH)2 nanosheets, facilitating faster charge transfer. Consequently, Zn/Co-S@Ni(OH)2 demonstrates remarkable electrochemical characteristics as an electrode material for supercapacitors with an area capacitance of 12.9 F cm-2 at a current density of 2 mA cm-2 in 2 M KOH. The assembled asymmetric supercapacitor device achieves a high energy density of 0.95 mW h cm-2, while showing excellent longevity with a retention of 90.9% over 5000 cycles. Additionally, the Zn/Co-S@Ni(OH)2 arrays demonstrate significant oxygen evolution reaction activity with an overpotential of 242 mV at 10 mA cm-2 in 1 M KOH and significant stability for more than 100 h. This work provides a valuable approach for synthesizing bifunctional electrode materials for both energy storage and electrocatalysis applications.