  The Transiting Exoplanet Survey Satellite (TESS) mission searches for new
exoplanets. The observing strategy of TESS results in high-precision photometry
of millions of stars across the sky, allowing for detailed asteroseismic
studies of individual systems. In this work, we present a detailed
asteroseismic analysis of the giant star HD 76920 hosting a highly eccentric
giant planet ($e = 0.878$) with an orbital period of 415 days, using 5 sectors
of TESS light curve that cover around 140 days of data. Solar-like oscillations
in HD 76920 are detected around $52 \, \mu$Hz by TESS for the first time. By
utilizing asteroseismic modeling that takes classical observational parameters
and stellar oscillation frequencies as constraints, we determine improved
measurements of the stellar mass ($1.22 \pm 0.11\, M_\odot$), radius ($8.68 \pm
0.34\,R_\odot$), and age ($5.2 \pm 1.4\,$Gyr). With the updated parameters of
the host star, we update the semi-major axis and mass of the planet as $a=1.165
\pm 0.035$ au and $M_{\rm p}\sin{i} = 3.57 \pm 0.22\,M_{\rm Jup}$. With an
orbital pericenter of $0.142 \pm 0.005$ au, we confirm that the planet is
currently far away enough from the star to experience negligible tidal decay
until being engulfed in the stellar envelope. We also confirm that this event
will occur within about 100\,Myr, depending on the stellar model used.
