  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.
