  The origin of the observed diversity of planetary system architectures is one
of the main topic of the exoplanetary research. The detection of a
statistically significant sample of planets around young stars allows us to
study the early stages of planet formation and evolution, but only a handful of
them is known so far. In this regard, a considerable contribution is expected
from the NASA TESS satellite, which is now performing a survey of $\sim 85 \%$
of the sky to search for short-period transiting planets In its first month of
operations, TESS found a planet candidate with an orbital period of 8.14 days
around a member of the Tuc-Hor young association ($\sim$ 40 Myr), the G6V main
component of the binary system DS\,Tuc. If confirmed, it would be the first
transiting planet around a young star suitable for radial velocity and/or
atmospheric characterization. We aim to validate the planetary nature of this
companion and to measure its orbital and physical parameters. We obtain
accurate planet parameters by coupling an independent reprocessing of the TESS
light curve with improved stellar parameters and the dilution caused by the
binary companion; we analyse high precision archival radial velocities to
impose an upper limit of about 0.1 M$_{\rm Jup}$ on the planet mass; we finally
rule out the presence of external companions beyond 40 au with adaptive optics
images. We confirm the presence of a young, giant (${\rm R} = 0.50$ R$_{\rm
Jup}$) planet having a not negligible possibility to be inflated (theoretical
mass $\lesssim 20$ M$_{\oplus}$) around DS\,Tuc~A. We discuss the feasibility
of mass determination, Rossiter-McLaughlin analysis and atmosphere
characterization, allowed by the brightness of the star.
