  Deep ALMA and HST observations reveal the presence of a quenched massive
galaxy within the $z=2.91$ galaxy group RO-1001. With a mass-weighted stellar
age of $1.6 \pm 0.4 \,$Gyr this galaxy is one of the oldest known at $z\sim3$,
implying that most of its $10^{11}\rm \, M_{\odot}$ of stars were rapidly
formed at $z>6$--8. This is a unique example of the predominantly passive
evolution of a galaxy over at least $3<z<6$ following its high-redshift
quenching and a smoking-gun event pointing to the early imprint of an
age-environment relation. At the same time, being in a dense group environment
with extensive cold-gas reservoirs as betrayed by a giant Ly$\alpha$ halo, the
existence of this galaxy demonstrates that gas accretion shutdown is not
necessary for quenching and its maintenance.
