Abstract A search for pair-produced vector-like quarks using events with exactly one lepton ( e or $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> ), at least four jets including at least one b -tagged jet, and large missing transverse momentum is presented. Data from proton–proton collisions at a centre-of-mass energy of $$\sqrt{s}=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 13 $$\text {TeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>TeV</mml:mtext> </mml:math> , recorded by the ATLAS detector at the LHC from 2015 to 2018 and corresponding to an integrated luminosity of 139 fb $$^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> , are analysed. Vector-like partners T and B of the top and bottom quarks are considered, as is a vector-like X with charge $$+5/3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>5</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> , assuming their decay into a W , Z , or Higgs boson and a third-generation quark. No significant deviations from the Standard Model expectation are observed. Upper limits on the production cross-section of T and B quark pairs as a function of their mass are derived for various decay branching ratio scenarios. The strongest lower limits on the masses are 1.59 $$\text {TeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>TeV</mml:mtext> </mml:math> assuming mass-degenerate vector-like quarks and branching ratios corresponding to the weak-isospin doublet model, and 1.47 $$\text {TeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>TeV</mml:mtext> </mml:math> (1.46 $$\text {TeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>TeV</mml:mtext> </mml:math> ) for exclusive $$T \rightarrow Zt$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>→</mml:mo> <mml:mi>Z</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> ( $$B/X \rightarrow Wt$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>/</mml:mo> <mml:mi>X</mml:mi> <mml:mo>→</mml:mo> <mml:mi>W</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> ) decays. In addition, lower limits on the T and B quark masses are derived for all possible branching ratios.