  We present the discovery of the radio afterglow of the short $\gamma$-ray
burst (GRB) 210726A, localized to a galaxy at a photometric redshift of $z\sim
2.4$. While radio observations commenced $\lesssim 1~$day after the burst, no
radio emission was detected until $\sim11~$days. The radio afterglow
subsequently brightened by a factor of $\sim 3$ in the span of a week, followed
by a rapid decay (a "radio flare"). We find that a forward shock afterglow
model cannot self-consistently describe the multi-wavelength X-ray and radio
data, 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 the
isotropic kinetic energy of the burst by a factor of $\approx 4$, or a reverse
shock from a shell collision are viable solutions to match the broad-band
behavior. At $z\sim 2.4$, GRB 210726A is among the highest redshift short GRBs
discovered to date as well as the most luminous in radio and X-rays. Combining
and comparing all previous radio afterglow observations of short GRBs, we find
that the majority of published radio searches conclude by $\lesssim 10~$days
after the burst, potentially missing these late rising, luminous radio
afterglows.
