  A search is made for a vector-like $T$ quark decaying into a Higgs boson and
a top quark in 13 TeV proton-proton collisions using the ATLAS detector at the
Large Hadron Collider with a data sample corresponding to an integrated
luminosity of 139 fb$^{-1}$. The Higgs-boson and top-quark candidates are
identified in the all-hadronic decay mode, where $H\to b\bar{b}$ and $t\to b W
\to b q \bar{q}^\prime$ are reconstructed as large-radius jets. The candidate
Higgs boson, top quark, and associated B-hadrons are identified using tagging
algorithms. No significant excess is observed above the background, so limits
are set on the production cross-section of a singlet $T$ quark at 95%
confidence level, depending on the mass, $m_T$, and coupling, $\kappa_T$, of
the vector-like $T$ quark to Standard Model particles. In the considered mass
range between 1.0 and 2.3 TeV, the upper limit on the allowed coupling values
increases with $m_T$ from a minimum value of 0.35 for 1.07 < $m_T$ < 1.4 TeV to
1.6 for $m_T$ = 2.3 TeV.
