  The Transiting Exoplanet Survey Satellite (TESS) is an all-sky survey mission
aiming to search for exoplanets that transit bright stars. The high-quality
photometric data of TESS are excellent for the asteroseismic study of
solar-like stars. In this work, we present an asteroseismic analysis of the
red-giant star HD~222076 hosting a long-period (2.4 yr) giant planet discovered
through radial velocities. Solar-like oscillations of HD~222076 are detected
around $203 \, \mu$Hz by TESS for the first time. Asteroseismic modeling, using
global asteroseismic parameters as input, yields a determination of the stellar
mass ($M_\star = 1.12 \pm 0.12\, M_\odot$), radius ($R_\star = 4.34 \pm
0.21\,R_\odot$), and age ($7.4 \pm 2.7\,$Gyr), with precisions greatly improved
from previous studies. The period spacing of the dipolar mixed modes extracted
from the observed power spectrum reveals that the star is on the red-giant
branch burning hydrogen in a shell surrounding the core. We find that the
planet will not escape the tidal pull of the star and be engulfed into it
within about $800\,$Myr, before the tip of the red-giant branch is reached.
