ABSTRACT The recently discovered super-Earth LP 890-9 c is an intriguing target for atmospheric studies as it transits a nearby, low-activity late-type M-dwarf star at the inner edge of the Habitable Zone. Its position at the runaway greenhouse limit makes it a natural laboratory to study the climate evolution of hot rocky planets. We present the first 3D-Global Climate Model exo-Venus model for a modern Venus-like atmosphere (92 bar surface pressure, realistic composition, and H2SO4 radiatively-active clouds), applied to the tidally-locked LP 890-9 c to inform observations by JWST and future instruments. If LP 890-9 c has developed into a modern exo-Venus, then the modelled temperatures suggest that H2SO4 clouds are possible even in the substellar region. Like on modern Venus, clouds on LP 890-9 c would create a flat spectrum. The strongest CO2 bands in transmission predicted by our model for LP 890-9 c are about 10 ppm, challenging detection, given JWST estimated noise floor. Estimated phase curve amplitudes are 0.9 and 2.4 ppm for continuum and CO2 bands, respectively. While pointing out the challenge to characterise modern exo-Venus analogues, these results provide new insights for JWST proposals and highlight the influence of clouds in the spectrum of hot rocky exoplanet spectra.