  The vectorlike top partners $T$ are predicted in many extensions of the
Standard Model (SM). In a simplified model including a single vectorlike $T$
quark with charge $2/3$, we investigate the process $pp \to Tj$ induced by the
couplings between the top partner with the first and the third generation
quarks at the LHC. We find that the mixing with the first generation can
enhance the production cross section. We further study the observability of the
single heavy top partner through the process $pp \to T(\to th)j\to t(\to b \ell
\nu_{\ell})h( \to \gamma\gamma) j$ at the high-luminosity~(HL)-LHC~(a 14 TeV
$pp$ collider with an integrated luminosity of 3 ab$^{-1}$). For three typical
heavy $T$ quark masses $m_T=600,800$ and 1000 GeV, the $3\sigma$ exclusion
limits, as well as the $5\sigma$ discovery reach in the parameter plane of the
two variables $g^{\ast}-R_L$, are respectively obtained at the HL-LHC.
