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.
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