Results from a wide range of searches targeting different experimental signatures with and without missing transverse momentum (E(T)^(miss)) are used to constrain a Two-Higgs-Doublet Model (2HDM) with an additional pseudo-scalar mediating the interaction between ordinary and dark matter (2HDM+a). The analyses use up to 139 fb^(-1) of proton-proton collision data at a centre-of-mass energy s=13 TeV recorded with the ATLAS detector at the Large Hadron Collider during 2015-2018. The results …