  A comprehensive multi-wavelength campaign has been carried out to probe
stellar activity and variability in the young Sun-like star $\iota$-Horologii.
We present the results from long-term spectropolarimetric monitoring of the
system by using the ultra-stable spectropolarimeter/velocimeter HARPS at the
ESO 3.6-m telescope. Additionally, we included high-precision photometry from
the NASA Transiting Exoplanet Survey Satellite (TESS) and observations in the
far- and near-ultraviolet spectral regions using the STIS instrument on the
NASA/ESA Hubble Space Telescope (HST). The high-quality dataset allows a robust
characterisation of the star's rotation period, as well as a probe of the
variability using a range of spectroscopic and photometric activity proxies. By
analyzing the gradient of the power spectra (GPS) of the TESS lightcurves we
constrained the faculae-to-spot driver ratio ($\rm S_{fac}/S_{spot}$) to
0.510$\pm$0.023, which indicates that the stellar surface is spot dominated
during the time of the observations. We compared the photospheric activity
properties derived from the GPS method with a magnetic field map of the star
derived using Zeeman-Doppler imaging (ZDI) from simultaneous
spectropolarimetric data for the first time. Different stellar activity proxies
enable a more complete interpretation of the observed variability. For example,
we observed enhanced emission in the HST transition line diagnostics C IV and C
III, suggesting a flaring event. From the analysis of TESS data acquired
simultaneously with the HST data, we investigate the photometric variability at
the precise moment that the emission increased and derive correlations between
different observables, probing the star from its photosphere to its corona.
