  A search for the single production of a vector-like top partner ($T$)
decaying into a $Z$ boson and a top quark is presented, using the full Run 2
dataset corresponding to 139 $\mathrm{fb}^{-1}$ of $pp$ collisions at $\sqrt{s}
= 13$ TeV, collected in 2015-2018 with the ATLAS detector at the Large Hadron
Collider. The targeted final state is characterized by the presence of a pair
of electrons or muons with opposite-sign charges which form a $Z$-boson
candidate, as well as by the presence of $b$-tagged jets and forward jets.
Events with exactly two or at least three leptons are categorized into two
independently optimized analysis channels. No significant excess above the
background expectation is observed and the results from the two channels are
statistically combined to set exclusion limits at 95% confidence level on the
masses and couplings of $T$ for different benchmark models and generalized
branching ratio scenarios.
