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We report the discovery of NGTS-21b, a massive hot Jupiter orbiting a low-mass star as part of the Next Generation Transit Survey (NGTS). The planet has a mass and radius of $2.36 \pm 0.21$ M$_{\rm J}$, and $1.33 \pm 0.03$ R$_{\rm J}$, and an orbital period of 1.543 days. The host is a K3V ($T_{\rm eff}=4660 \pm 41$, K) metal-poor (${\rm [Fe/H]}=-0.26 \pm 0.07$, dex) dwarf star with a mass and radius of $0.72 \pm 0.04$, M$_{\odot}$,and $0.86 \pm 0.04$, R$_{\odot}$. Its age and rotation period of $10.02^{+3.29}_{-7.30}$, Gyr and $17.88 \pm 0.08$, d respectively, are in accordance with the observed moderately low stellar activity level. When comparing NGTS-21b with currently known transiting hot Jupiters with similar equilibrium temperatures, it is found to have one of the largest measured radii despite its large mass. Inflation-free planetary structure models suggest the planet's atmosphere is inflated by $\sim21\%$, while inflationary models predict a radius consistent with observations, thus pointing to stellar irradiation as the probable origin of NGTS-21b's radius inflation. Additionally, NGTS-21b's bulk density ($1.25 \pm 0.15$, g/cm$^3$) is also amongst the largest within the population of metal-poor giant hosts ([Fe/H] < 0.0), helping to reveal a falling upper boundary in metallicity-planet density parameter space that is in concordance with core accretion formation models. The discovery of rare planetary systems such as NGTS-21 greatly contributes towards better constraints being placed on the formation and evolution mechanisms of massive planets orbiting low-mass stars.