We report deep imaging observations with DOLoRes@TNG of an ultra-faint dwarf satellite candidate of the Triangulum galaxy (M33) found by visual inspection of the public imaging data release of the DESI Legacy Imaging Surveys. Pisces VII/Triangulum (Tri) III is found at a projected distance of $72\, {\rm kpc}$ from M33, and using the tip of the red giant branch method, we estimate a distance of $D=1.0^{+0.3}_{-0.2}\, {\rm Mpc}$, meaning the galaxy could either be an isolated ultra-faint or the second known satellite of M33. We estimate an absolute magnitude of MV = -6.1 ± 0.2 if Pisces VII/Tri II is at the distance of M33, or as bright as MV = -6.8 ± 0.2 if the galaxy is isolated. At the isolated distance, it has a physical half-light radius of $r_{\rm h}=131\pm 61\, {\rm pc}$ consistent with similarly faint galaxies around the Milky Way. As the tip of the red giant branch is sparsely populated, constraining a precision distance is not possible, but if Pisces VII/Tri III can be confirmed as a true satellite of M33, it is a significant finding. With only one potential satellite detected around M33 previously (Andromeda XXII/Tri I), it lacks a significant satellite population in stark contrast to the similarly massive Large Magellanic Cloud. The detection of more satellites in the outskirts of M33 could help to better illuminate if this discrepancy between expectation and observations is due to a poor understanding of the galaxy formation process, or if it is due to the low luminosity and surface brightness of the M33 satellite population which has thus far fallen below the detection limits of previous surveys. If it is truly isolated, it would be the faintest known field dwarf detected to date.