The UV aurorae of Uranus, suspected in IUE observations {1982-1986}, were only unambiguously identified during the Voyager 2 flyby {1986}. Their peculiar properties relate to the atypical magnetosphere of Uranus, which is characteristic of ice giants. In contrast with the solstice configuration prevailing in the 1980s, that only allowed the northern magnetic pole to be visible from Earth, the situation is now radically different and near-equinoctial conditions allow views of both northern {N} and southern {S} poles transiting across the visible disc, implying a dynamic magnetospheric configuration that has never been studied. We therefore propose to re-attempt to observe the UV aurorae of Uranus with HST spectroscopic {STIS} and imaging {ACS} measurements. We will maximize the probability of detection by scheduling observations of Uranus during a solar wind shock interaction, known to activate auroral activity at other planets. Observations will be distributed over 14 days, centered on the predicted arrival time, and sampling all longitudes. They will characterize the UV aurorae, determine their brightness {and infer the energy of precipitating electrons}, their location and their temporal variability up to half a solar rotation. Importantly, it will also permit us to retrieve the rotational phase of the planet and update the rotation period {17.24h}. Observations during an interplanetary shock and comparisons with Voyager 2 and previous unsucessful HST observations will finally provide the first insights into the sun/magnetosphere interaction, and highlight its difference with the interaction at the other known magnetospheres.