Properties of the underlying-event in pp interactions are investigated primarily via the strange hadrons $$K_{S}^{0}$$ K S 0 , $$\Lambda $$ Λ and $$\bar{\Lambda }$$ Λ ¯ , as reconstructed using the ATLAS detector at the LHC in minimum-bias pp collision data at $$\sqrt{s} = 13$$ s = 13 TeV. The hadrons are reconstructed via the identification of the displaced two-particle vertices corresponding to the decay modes "Equation missing", $$\Lambda \rightarrow \pi ^-p$$ Λ → π - p and $$\bar{\Lambda }\rightarrow \pi ^+\bar{p}$$ Λ ¯ → π + p ¯ . These are used in the construction of underlying-event observables in azimuthal regions computed relative to the leading charged-particle jet in the event. None of the hadronisation and underlying-event physics models considered can describe the data over the full kinematic range considered. Events with a leading charged-particle jet in the range of $$10 < p_T \le 40$$ 10 < p T ≤ 40 GeV are studied using the number of prompt charged particles in the transverse region. The ratio $$N(\Lambda + \bar{\Lambda })/N(K_{S}^{0})$$ N ( Λ + Λ ¯ ) / N ( K S 0 ) as a function of the number of such charged particles varies only slightly over this range. This disagrees with the expectations of some of the considered Monte Carlo models.