  We present the discovery of TOI-197.01, the first transiting planet
identified by the Transiting Exoplanet Survey Satellite (TESS) for which
asteroseismology of the host star is possible. TOI-197 (HIP116158) is a bright
(V=8.2 mag), spectroscopically classified subgiant which oscillates with an
average frequency of about 430 muHz and displays a clear signature of mixed
modes. The oscillation amplitude confirms that the redder TESS bandpass
compared to Kepler has a small effect on the oscillations, supporting the
expected yield of thousands of solar-like oscillators with TESS 2-minute
cadence observations. Asteroseismic modeling yields a robust determination of
the host star radius (2.943+/-0.064 Rsun), mass (1.212 +/- 0.074 Msun) and age
(4.9+/-1.1 Gyr), and demonstrates that it has just started ascending the
red-giant branch. Combining asteroseismology with transit modeling and
radial-velocity observations, we show that the planet is a "hot Saturn"
(9.17+/-0.33 Rearth) with an orbital period of ~14.3 days, irradiance of
343+/-24 Fearth, moderate mass (60.5 +/- 5.7 Mearth) and density (0.431+/-0.062
gcc). The properties of TOI-197.01 show that the host-star metallicity - planet
mass correlation found in sub-Saturns (4-8 Rearth) does not extend to larger
radii, indicating that planets in the transition between sub-Saturns and
Jupiters follow a relatively narrow range of densities. With a density measured
to ~15%, TOI-197.01 is one of the best characterized Saturn-sized planets to
date, augmenting the small number of known transiting planets around evolved
stars and demonstrating the power of TESS to characterize exoplanets and their
host stars using asteroseismology.
