We present the discovery of HD 221416 b, the first transiting planet identified by the Transiting Exoplanet Survey Satellite (TESS) for which asteroseismology of the host star is possible. HD 221416 b (HIP 116158, TOI-197) is a bright (V=8.2 mag), spectroscopically classified subgiant that oscillates with an average frequency of about 430 μHz 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 (R å =2.943±0.064 R e), mass (M å =1.212±0.074 M e), 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" (R p =9.17±0.33 R ⊕) with an orbital period of ∼14.3 days, irradiance of F=343±24 F ⊕ , and moderate mass (M p =60.5±5.7 M ⊕) and density (ρ p =0.431±0.062 g cm −3). The properties of HD 221416 b show that the host-star metallicity-planet mass correlation found in sub-Saturns (4-8 R ⊕) 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%, HD 221416 b is one of the best characterized Saturn-size 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.