We study the IB(s)m galaxy IC 3476 observed in the context of the Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE), a blind narrow-band H{alpha}+[NII] imaging survey of the Virgo cluster carried out with MegaCam at the CFHT. The deep narrow-band image reveals a very pertubed ionised gas distribution that is characterised by a prominent banana-shaped structure in the front of the galaxy formed of giant HII regions crossing the stellar disc. Star-forming structures, at ~8kpc from the edges of the stellar disc, are also detected in a deep far-ultraviolet ASTROSAT/UVIT image. This particular morphology indicates that the galaxy is undergoing an almost edge-on ram pressure stripping event. The same H{alpha}+[NII] image also shows that the star formation activity is totally quenched in the leading edge of the disc, where the gas has been removed during the interaction with the surrounding medium. The spectral energy distribution fitting analysis of the multi-frequency data indicates that this quenching episode is very recent (~50Myr), and roughly corresponds to an increase of the star formation activity by a factor of ~161% in the inner regions with respect to that expected for secular evolution. The analysis of these data, whose angular resolution enables the study of the induced effects of the perturbation down to the scale of individual HII regions (r_eq_~=40pc), also suggests that the increase of star formation activity is due to the compression of the gas along the stellar disc of the galaxy, which is able to increase its mean electron density and boost the star formation process producing bright HII regions with luminosities up to L(H{alpha})~=10^38^erg/s. The combined analysis of the VESTIGE data with deep IFU spectroscopy gathered with MUSE and with high spectral resolution Fabry Perot data also indicates that the hydrodynamic interaction has deeply perturbed the velocity field of the ionised gas component while leaving that of the stellar disc unaffected. The comparison of the data with tuned high-resolution hydrodynamic simulations accounting for the different gas phases (atomic, molecular, ionised) consistently indicates that the perturbing event is very recent (50-150Myr), once again confirming that ram pressure stripping is a violent phenomenon that is able to perturb the evolution of galaxies in rich environments on short timescales.