  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-GCM exo-Venus model for a modern
Venus-like atmosphere (92 bar surface pressure, realistic composition,
H$_2$SO$_4$ radiatively-active clouds), applied to the tidally-locked LP 890-9c
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
H$_2$SO$_4$ 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 CO$_2$
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 CO$_2$ 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.
