We present the discovery of a white dwarf companion at similar to 3.6 arcsec from GJ 3346, a nearby (pi similar to 42 mas) K star observed with SPHERE@VLT as part of an open time survey for faint companions to objects with significant proper motion discrepancies (Delta mu) between Gaia DR1 and Tycho-2. Syrius-like systems like GJ 3346 AB, which include a main-sequence star and a white dwarf, can be difficult to detect because of the intrinsic faintness of the latter. They have, however, been found to be common contaminants for direct imaging (DI) searches. White dwarfs have in fact similar brightness to substellar companions in the infrared, while being much brighter in the visible bands like those used by Gaia. Combining our observations with Gaia DR2 and with several additional archival data sets, we were able to fully constrain the physical properties of GJ 3346 B, such as its effective temperature (11 x 10(3) +/- 500 K) as well as the cooling age of the system (648 +/- 58 Myr). This allowed us to better understand the system history and to partially explain the discrepancies previously noted in the age indicators for this object. Although further investigation is still needed, it seems that GJ 3346, which was previously classified as young, is in fact most likely to be older than 4 Gyr. Finally, given that the mass (0.58 +/- 0.01 M-circle dot) and separation (85 au) of GJ 3346 B are compatible with the observed Delta mu, this discovery represents a further confirmation of the potential of this kind of dynamical signatures as selection methods for DI surveys targeting faint, substellar companions.