A search for a heavy CP-odd Higgs boson, A, decaying into a Z boson and a heavy CP-even Higgs boson, H, is presented. It uses the full LHC Run 2 dataset of pp collisions at $ \sqrt{s} $ = 13 TeV collected with the ATLAS detector, corresponding to an integrated luminosity of 140 fb$^{−1}$. The search for A → ZH is performed in the $ {\ell}^{+}{\ell}^{-}t\overline{t} $ and $ \nu \overline{\nu}b\overline{b} $ final states and surpasses the reach of previous searches in different final states in the region with m$_{H}$ > 350 GeV and m$_{A}$ > 800 GeV. No significant deviation from the Standard Model expectation is found. Upper limits are placed on the production cross-section times the decay branching ratios. Limits with less model dependence are also presented as functions of the reconstructed m($ t\overline{t} $) and m($ b\overline{b} $) distributions in the $ {\ell}^{+}{\ell}^{-}t\overline{t} $ and $ \nu \overline{\nu}b\overline{b} $ channels, respectively. In addition, the results are interpreted in the context of two-Higgs-doublet models.[graphic not available: see fulltext]