Abstract: A search for a new heavy scalar particle X decaying into a Standard Model (SM) Higgs boson and a new singlet scalar particle S is presented. The search uses a proton-proton (pp) collision data sample with an integrated luminosity of 140 fb(-1) recorded at a centre-of-mass energy of root s = 13 TeV with the ATLAS detector at the Large Hadron Collider. The most sensitive mass parameter space is explored in X mass ranging from 500 to 1500 GeV, with the corresponding S mass in the range 200-500 GeV. The search selects events with two hadronically decaying tau-lepton candidates from H -> tau(+)tau(-) decays and one or two light leptons (l = e, mu) from S -> VV (V = W, Z) decays while the remaining V boson decays hadronically or to neutrinos. A multivariate discriminant based on event kinematics is used to separate the signal from the background. No excess is observed beyond the expected SM background and 95% confidence level upper limits between 72 fb and 542 fb are derived on the cross-section sigma(pp -> X -> SH) assuming the same SM-Higgs boson-like decay branching ratios for the S -> VV decay. Upper limits on the visible cross-sections sigma(pp -> X -> SH -> WW tau tau) and sigma(pp -> X -> SH -> ZZ tau tau) are also set in the ranges 3-26 fb and 6-33 fb, respectively.