We study the IB(s)m galaxy IC 3476 observed in the context of VESTIGE, a blind narrow-band Halpha+[NII] imaging survey of the Virgo cluster. The deep narrow-band (NB) image reveals a very pertubed ionised gas distribution, characterised by a prominent banana-shaped structure in the front of the galaxy formed of giant HII regions crossing the stellar disc, with star forming structures at ~8 kpc from the edges of the stellar disc, detected also in a deep FUV ASTROSAT/UVIT image. This particular morphology indicates that the galaxy is undergoing an almost edge-on ram pressure stripping event. The NB 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. The SED fitting analysis indicates that this quenching episode is very recent (~50 Myr), and roughly corresponds to an increase of the star formation activity in the inner regions with respect to what expected for secular evolution. The analysis of these data, whose angular resolution allows the study of the induced effects of the perturbation down to the scale of individual HII regions, also suggests that the increase of the 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. The hydrodynamic interaction has deeply perturbed the velocity field of the ionised gas component while leaving unaffected that of the stellar disc. The comparison of the data with hydrodynamic simulations accounting for the different gas phases (atomic, molecular, ionised) consistently indicates that the perturbing event is very recent, once again confirming that ram pressure stripping is a violent phenomenon able to perturb on short timescales the evolution of galaxies in rich environments.