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We report the discovery of a relic Giant Radio Galaxy (GRG) J021659-044920 atredshift $z \sim 1.3$ that exhibits large-scale extended, nearly co-spatial,radio and X-ray emission from radio lobes, but no detection of Active GalacticNuclei core, jets and hotspots. The total angular extent of the GRG at theobserved frame 0.325 GHz, using Giant Metrewave Radio Telescope observations isfound to be ${\sim}$ 2.4 arcmin, that corresponds to a total projected linearsize of $\sim$ 1.2 Mpc. The integrated radio spectrum between 0.240 and 1.4 GHzshows high spectral curvature (${\alpha}_{\rm 0.610~GHz}^{\rm 1.4~GHz} -{\alpha}_{\rm 0.240~GHz}^{\rm 0.325~GHz}$ $>$ 1.19) with sharp steepening above0.325 GHz, consistent with relic radio emission that is $\sim$ 8 $\times$10$^{6}$ yr old. The radio spectral index map between observed frame 0.325 and1.4~GHz for the two lobes varies from 1.4 to 2.5 with the steepening trend fromouter-end to inner-end, indicating backflow of plasma in the lobes. Theextended X-ray emission characterized by an absorbed power-law with photonindex $\sim$ 1.86 favours inverse-Compton scattering of the Cosmic MicrowaveBackground (ICCMB) photons as the plausible origin. Using both X-ray and radiofluxes under the assumption of ICCMB we estimate the magnetic field in thelobes to be 3.3 $\mu$G. The magnetic field estimate based on energyequipartition is $\sim$ 3.5 $\mu$G. Our work presents a case study of a rareexample of a GRG caught in dying phase in the distant Universe.

J021659-044920: a relic giant radio galaxy at z ~ 1.3