We present the first transmission spectroscopy study of an exoplanet atmosphere with the high-resolution mode of the new Gemini High-resolution Optical SpecTrograph (GHOST) instrument at the Gemini South Observatory. We observed one transit of HAT-P-70 b-an ultra-hot Jupiter with an inflated radius-and made a new detection of the infrared Ca ii triplet in its transmission spectrum. The depth of the strongest line implies that a substantial amount of Ca ii extends to at least 47% above the bulk planetary radius. The triplet lines are blueshifted between similar to 3 to 5 km s-1, indicative of strong dayside-to-nightside winds common on highly irradiated gas giants. Comparing the transmission spectrum with atmospheric models that incorporate non-local thermodynamic equilibrium effects suggests that the planetary mass is likely between 1 and 2 MJ, much lighter than the upper limit previously derived from radial velocity measurements. Importantly, thanks to the high signal-to-noise ratio achieved by GHOST/Gemini South, we are able to measure the temporal variation of these signals. Absorption depths and velocity offsets of the individual Ca ii lines remain mostly consistent across the transit, except for the egress phases, where weaker absorption and stronger blueshifts are observed, highlighting the atmospheric processes within the trailing limb alone. Our study demonstrates the ability of GHOST to make time-resolved detections of individual spectral lines, providing valuable insights into the 3D nature of exoplanet atmospheres by probing different planetary longitudes as the tidally locked planet rotates during the transit.