The recent detection of TeV photons from two gamma-ray bursts (GRBs), GRB 190114C and GRB 180720B, has opened a new window for multi-messenger and multi-wavelength astrophysics of high-energy transients. We study the origin of very-high-energy (VHE) $gamma$-rays from the short GRB 160821B, for which the MAGIC Collaboration reported a $sim 3 sigma$ statistical significance. Short GRBs are often accompanied by extended and plateau emission, which is attributed to internal dissipation resulting from activities of a long-lasting central engine, and Murase et al. (2018) recently suggested the external inverse-Compton (EIC) scenario for VHE counterparts of short GRBs and neutron star mergers. Applying this scenario to GRB 160821B, we show that the EIC flux can reach $sim 10^{-12}rm~erg~cm^{-2}~s^{-1}$ within a time period of $sim 10^3 - 10^4rm~s$, which is consistent with the MAGIC observations. EIC $gamma$-rays expected during the extended and plateau emission will be detectable with greater significance by future detectors such as the Cherenkov Telescope Array (CTA). The resulting light curve has a distinguishable feature, where the VHE emission is predicted to reach the peak around the end of the seed emission.
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