  In this paper we present our project that aims at determining accurate
distances and proper motions for the Y brown dwarf population using the Hubble
Space Telescope. We validate the program with our first results, using a single
new epoch of observations of the Y0pec dwarf WISE J163940.83$-$684738.6. These
new data allowed us to refine its proper motion and improve the accuracy of its
parallax by a factor of three compared to previous determinations, now
constrained to $\varpi = 211.11 \pm 0.56$ mas. This newly derived absolute
parallax corresponds to a distance of $4.737 \pm 0.013$ pc, an exquisite and
unprecedented precision for faint ultracool Y dwarfs.
