  Using a first-principles approach based on density functional theory and
dynamical mean field theory, we study the electronic properties of a new
candidate polar metal SrEuMo$_2$O$_6$. Its electronic structure shares
similarities with centrosymmetric SrMoO$_3$ and EuMoO$_3$, from which it may be
considered an ordered derivative, but ferroelectric-like distortions of the
divalent cations and oxygen anions lift inversion symmetry mediated by an
anharmonic lattice interaction in the metallic state. We find that Hund's
coupling promotes the effects of electronic correlations owing to the Mo$^{4+}$
$d^{2}$ electronic configuration, producing a correlated metallic phase far
from the Mott state. The contraindication between metallicity and polar
distortions is thereby alleviated through the renormalized quasiparticles,
which are unable to fully screen the ordered local dipoles.
