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 $v_r=-363.4pm1.0,{rm kms}^{-1}$ and a velocity dispersion of $sigma_v=6.1^{+1.0}_{-0.9},{rm kms}^{-1}$, consistent with previous work and within $1sigma$ of predictions made within the modified Newtonian dynamics framework. We also measure the metallicity of our member stars from their spectra, finding a mean value of ${rm [Fe/H]}=-1.7pm0.1$~dex. We model the dark matter density profile of And~XXI using an improved version of GravSphere, finding a central density of $rho_{rm DM}({rm 150 pc})=2.7_{-1.7}^{+2.7} times 10^7 ,{rm M_odot,kpc^{-3}}$ at 68% confidence, and a density at two half light radii of $rho_{rm DM}({rm 1.75 kpc})=0.9_{-0.2}^{+0.3} times 10^5 ,{rm M_odot,kpc^{-3}}$ at 68% confidence. These are both a factor ${sim}3-5$ 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~XXIs low density can be accommodated within $Lambda$CDM if it experienced extreme tidal stripping (losing $>95%$ of its mass), or if it inhabits a low concentration halo on a plunging orbit that experienced repeated tidal shocks.
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