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We present the discovery of the radio afterglow of the short $\gamma$-rayburst (GRB) 210726A, localized to a galaxy at a photometric redshift of $z\sim2.4$. While radio observations commenced $\lesssim 1~$day after the burst, noradio emission was detected until $\sim11~$days. The radio afterglowsubsequently brightened by a factor of $\sim 3$ in the span of a week, followedby a rapid decay (a "radio flare"). We find that a forward shock afterglowmodel cannot self-consistently describe the multi-wavelength X-ray and radiodata, and underpredicts the flux of the radio flare by a factor of $\approx 5$.We find that the addition of substantial energy injection, which increases theisotropic kinetic energy of the burst by a factor of $\approx 4$, or a reverseshock from a shell collision are viable solutions to match the broad-bandbehavior. At $z\sim 2.4$, GRB 210726A is among the highest redshift short GRBsdiscovered to date as well as the most luminous in radio and X-rays. Combiningand comparing all previous radio afterglow observations of short GRBs, we findthat the majority of published radio searches conclude by $\lesssim 10~$daysafter the burst, potentially missing these late rising, luminous radioafterglows.

A Radio Flare in the Long-Lived Afterglow of the Distant Short GRB 210726A: Energy Injection or a Reverse Shock from Shell Collisions?