  We present new empirical infrared Period-Luminosity-Metallicity (PLZ) and
Period-Wesenheit-Metallicity (PWZ) relations for RR Lyrae based on the latest
Gaia EDR3 parallaxes. The relations are provided in the WISE $W1$ and $W2$
bands, as well as in the $W(W1, V - W1)$ and $W(W2, V - W2)$ Wesenheit
magnitudes. The relations are calibrated using a very large sample of Galactic
halo field RR Lyrae stars with homogeneous spectroscopic [Fe/H] abundances
(over 1,000 stars in the $W1$ band), covering a broad range of metallicities
($-2.5 \lesssim \textrm{[Fe/H]} \lesssim 0.0$). We test the performance of our
PLZ and PWZ relations by determining the distance moduli of both galactic and
extragalactic stellar associations: the Sculptor dwarf spheroidal galaxy in the
Local Group (finding $\bar{\mu}_{0}=19.47 \pm 0.06$), the Galactic globular
clusters M4 ($\bar{\mu}_{0}=11.16 \pm 0.05$) and the Reticulum globular cluster
in the Large Magellanic Cloud ($\bar{\mu}_{0}=18.23 \pm 0.06$). The distance
moduli determined through all our relations are internally self-consistent
(within $\lesssim$ 0.05 mag) but are systematically smaller (by $\sim$
2-3$\sigma$) than previous literature measurements taken from a variety of
methods/anchors. However, a comparison with similar recent RR Lyrae empirical
relations anchored with EDR3 likewise shows to varying extents a systematically
smaller distance modulus for PLZ/PWZ RR Lyrae relations.
