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 mu Hz 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-* = 2.943 +/- 0.064 R-circle dot), mass (M-* = 1.212 +/- 0.074 M-circle dot), 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-circle plus) with an orbital period of similar to 14.3 days, irradiance of F = 343 +/- 24 F-circle plus, and moderate mass (M-p = 60.5 +/- 5.7 M-circle plus) and density (rho(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-circle plus) 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 similar 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.