Andromeda XXI (And XXI) has been proposed as a dwarf spheroidal galaxy with a central dark matter density that is lower than expected in the standard |$\Lambda$| cold dark matter (⁠|$\Lambda$|CDM) cosmology. In this work, we present dynamical observations for 77 member stars in this system, more than doubling previous studies to determine whether this galaxy is truly a low-density outlier. We measure a systemic velocity of |$v_r=-363.4\pm 1.0{\rm \, km\, s^{-1}}$| and a velocity dispersion of |$\sigma _v=6.1^{+1.0}_{-0.9}{\rm \, km\, s^{-1}}$|⁠, consistent with previous work and within |$1\sigma$| of predictions made using the modified Newtonian dynamics framework. We also measure the metallicity of our member stars from their spectra, finding a mean value of |${\rm [Fe/H]}=-1.7\pm 0.1$| dex. We model the dark matter density profile of And XXI using an improved version of gravsphere, finding a central density of |$\rho _{\rm DM}({\rm 150 pc})=2.6_{-1.5}^{+2.4} \times 10^7 \, {\rm M_\odot \, kpc^{-3}}$| at 68 per cent confidence, and a density at two half-light radii of |$\rho _{\rm DM}({\rm 1.75 kpc})=0.9_{-0.2}^{+0.3} \times 10^6 \, {\rm M_\odot \, kpc^{-3}}$| at 68 per cent confidence. These are both a factor of|${\sim }3\!-\!5$| lower than the densities expected from abundance matching in |$\Lambda$|CDM. We show that this cannot be explained by ‘dark matter heating’ since And XXI had too little star formation to significantly lower its inner dark matter density, while dark matter heating only acts on the profile inside the half-light radius. However, And XXI’s low density can be accommodated within |$\Lambda$|CDM if it experienced extreme tidal stripping (losing |${\gt}95{{\ \rm per\ cent}}$| of its mass), or if it inhabits a low-concentration halo on a plunging orbit that experienced repeated tidal shocks.