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In this study, we investigate the effect of small amounts of zirconium alloying the medium-entropy alloy (TiVNb)₈₅Cr₁₅, a promising material for hydrogen storage. Alloys with 1, 4, and 7 at.% of Zr were prepared by arc melting and found to be multiphase, comprising at least three phases, indicating that Zr addition does not stabilize a single-phase solid solution. The dominant BCC phase (<b>HEA₁</b>) is the primary hydrogen absorber, while the minor phases <b>HEA₂</b> and <b>HEA₃</b> play a crucial role in hydrogen absorption/desorption. Among the studied alloys, <span style="color: #169179;"><b>Zr4</b> </span>(TiVNb)₈₁Cr₁₅Zr₄ shows the highest hydrogen storage capacity, ease of activation, and reversibly retrievable hydrogen. This alloy can absorb hydrogen at room temperature without additional processing, with a reversible capacity of up to 0.74 wt.%, corresponding to hydrogen-to-metal ratio H/M = 0.46. The study emphasizes the significant role of minor elemental additions in alloy properties, stressing the importance of tailored compositions for hydrogen storage applications. It suggests a direction for further research in metal hydride alloys for effective and safe hydrogen storage.