We observed the late-Type peculiar galaxy NGC 4424 during the Virgo Environmental Survey Tracing Galaxy Evolution (VESTIGE), a blind narrow-band Hα+[NII] imaging survey of the Virgo cluster carried out with MegaCam at the Canada-French-Hawaii Telescope (CFHT). The presence of a ∼110 kpc (in projected distance) HI tail in the southern direction indicates that this galaxy is undergoing a ram pressure stripping event. The deep narrow-band image revealed a low surface brightness (Σ(Hα) â 4 × 10-18 erg s-1 cm-2 arcsec-2) ionised gas tail ∼10 kpc in length extending from the centre of the galaxy to the north-west, thus in the direction opposite to the HI tail. Chandra and XMM X-rays data do not show a compact source in the nucleus or an extended tail of hot gas, while IFU spectroscopy (MUSE) indicates that the gas is photo-ionised in the inner regions and shock-ionised in the outer parts. Medium-resolution (MUSE) (MUSE) indicates that the gas is photo-ionised in the inner regions and shock-ionised in the outer parts. Medium-resolution (MUSE) and high-resolution (Fabry-Perot) IFU spectroscopy confirms that the ionised gas is kinematically decoupled from the stellar component and indicates the presence of two kinematically distinct structures in the stellar disc. The analysis of the SED of the galaxy indicates that the activity of star formation was totally quenched in the outer disc ∼250-280 Myr ago, while only reduced by ∼80% in the central regions. All this observational evidence suggests that NGC 4424 is the remnant of an unequal-mass merger that occurred â 500 Myr ago when the galaxy was already a member of the Virgo cluster, and is now undergoing a ram pressure stripping event that has removed the gas and quenched the activity of star formation in the outer disc. The tail of ionised gas probably results from the outflow produced by a central starburst fed by the collapse of gas induced by the merging episode. This outflow is sufficiently powerful to overcome the ram pressure induced by the intracluster medium on the disc of the galaxy crossing the cluster. This analysis thus suggests that feedback can participate in the quenching process of galaxies in high-density regions.