A search is conducted for a new scalar boson S, with a mass distinct from that of the Higgs boson, decaying promptly into four leptons (ℓ=e, μ) via an intermediate state containing two on-shell, promptly decaying new spin-1 bosons Zd: S→ZdZd→4ℓ, where the Zd boson has a mass between 15 and 300 GeV, and the S boson has a mass between either 30 and 115 GeV or 130 and 800 GeV. The search uses proton–proton collision data collected with the ATLAS detector at the Large Hadron Collider with an integrated luminosity of 139 fb−1 at a centre-of-mass energy of s=13 TeV. No significant excess above the Standard Model background expectation is observed. Upper limits at 95% confidence level are set on the production cross-section times branching ratio, σ(gg→S)×B(S→ZdZd→4ℓ), as a function of the mass of both particles, mS and mZd.