ABSTRACT We present spatially resolved Echelle spectroscopy of an intervening Mg ii–Fe ii–Mg i absorption-line system detected at zabs = 0.73379 towards the giant gravitational arc PSZ1 G311.65–18.48. The absorbing gas is associated with an inclined disc-like star-forming galaxy, whose major axis is aligned with the two arc-segments reported here. We probe in absorption the galaxy’s extended disc continuously, at ≈3 kpc sampling, from its inner region out to 15× the optical radius. We detect strong ($W_0^{2796}\gt 0.3$Å) coherent absorption along 13 independent positions at impact parameters D = 0–29 kpc on one side of the galaxy, and no absorption at D = 28–57 kpc on the opposite side (all de-lensed distances at zabs). We show that (1) the gas distribution is anisotropic; (2) $W_0^{2796}$, $W_0^{2600}$, $W_0^{2852}$, and the ratio $W_0^{2600}\!/W_0^{2796}$, all anticorrelate with D; (3) the $W_0^{2796}$–D relation is not cuspy and exhibits significantly less scatter than the quasar-absorber statistics; (4) the absorbing gas is co-rotating with the galaxy out to D ≲ 20 kpc, resembling a ‘flat’ rotation curve, but at D ≳ 20 kpc velocities decline below the expectations from a 3D disc-model extrapolated from the nebular O ii emission. These signatures constitute unambiguous evidence for rotating extra-planar diffuse gas, possibly also undergoing enriched accretion at its edge. Arguably, we are witnessing some of the long-sought processes of the baryon cycle in a single distant galaxy expected to be representative of such phenomena.