  New insights on stellar evolution and stellar interiors physics are being
made possible by asteroseismology. Throughout the course of the Kepler mission,
asteroseismology has also played an important role in the characterization of
exoplanet-host stars and their planetary systems. The upcoming NASA Transiting
Exoplanet Survey Satellite (TESS) will be performing a near all-sky survey for
planets that transit bright nearby stars. In addition, its excellent
photometric precision, combined with its fine time sampling and long intervals
of uninterrupted observations, will enable asteroseismology of solar-type and
red-giant stars. Here we develop a simple test to estimate the detectability of
solar-like oscillations in TESS photometry of any given star. Based on an
all-sky stellar and planetary synthetic population, we go on to predict the
asteroseismic yield of the TESS mission, placing emphasis on the yield of
exoplanet-host stars for which we expect to detect solar-like oscillations.
This is done for both the target stars (observed at a 2-min cadence) and the
full-frame-image stars (observed at a 30-min cadence). A similar exercise is
also conducted based on a compilation of known host stars. We predict that TESS
will detect solar-like oscillations in a few dozen target hosts (mainly
subgiant stars but also in a smaller number of F dwarfs), in up to 200
low-luminosity red-giant hosts, and in over 100 solar-type and red-giant known
hosts, thereby leading to a threefold improvement in the asteroseismic yield of
exoplanet-host stars when compared to Kepler's.
