  We use data from the Multi-Unit Spectroscopic Explorer (MUSE), recently
commissioned at the Very Large Telescope (VLT), to study the kinematics and
stellar population content of NGC 4371, an early-type massive barred galaxy in
the core of the Virgo cluster. We integrate this study with a detailed
structural analysis using imaging data from the Hubble and Spitzer space
telescopes, which allows us to perform a thorough investigation of the physical
properties of the galaxy. We show that the rotationally supported inner
components in NGC 4371, an inner disc and a nuclear ring - which, according to
the predominant scenario, are built with stars formed from gas brought to the
inner region by the bar - are vastly dominated by stars older than 10 Gyr. Our
results thus indicate that the formation of the bar occurred at a redshift of
about $z=1.8^{+0.5}_{-0.4}$ (error bars are derived from 100 Monte Carlo
realisations). NGC 4371 thus testifies to the robustness of bars. In addition,
the mean stellar age of the fraction of the major disc of the galaxy covered by
our MUSE data is above 7 Gyr, with a small contribution from younger stars.
This suggests that the quenching of star formation in NGC 4371, likely due to
environmental effects, was already effective at a redshift of about
$z=0.8^{+0.2}_{-0.1}$. Our results point out that bar-driven secular evolution
processes may have an extended impact in the evolution of galaxies, and thus on
the properties of galaxies as observed today, not necessarily restricted to
more recent cosmic epochs.
