We present the discovery of the radio afterglow of the short γ-ray
burst (GRB) 210726A, localized to a galaxy at a photometric redshift of z∼2.4. While radio observations commenced ≲1day after the burst, no
radio emission was detected until ∼11~days. The radio afterglow
subsequently brightened by a factor of ∼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 ≈5.
We find that the addition of substantial energy injection, which increases the
isotropic kinetic energy of the burst by a factor of ≈4, or a reverse
shock from a shell collision are viable solutions to match the broad-band
behavior. At z∼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 ≲10days
after the burst, potentially missing these late rising, luminous radio
afterglows.Comment: 28 pages, 10 figures, submitted to Ap