A combination of measurements of associated production of a Standard Model Higgs boson with an electroweak gauge boson, $W$ or $Z$, is presented, targeting Higgs boson decays to bottom quarks and $W$ or $Z$ boson decays to leptons. The measurements that enter the combination were optimised for different regimes of the transverse momentum of the $W$ or $Z$ boson and reconstruct the Higgs boson candidate as two individual jets or a single large-radius jet. The measurements use proton-proton collision data produced by the Large Hadron Collider at a centre-of-mass energy of $\sqrt{s}=13$~TeV and collected with the ATLAS experiment between 2015 and 2018. The data set corresponds to an integrated luminosity of $139$~fb$^{-1}$. Cross-sections are measured in fiducial volumes as defined by the simplified template cross-section framework. The cross-sections are extracted in several categories of transverse momentum of the $W$ and $Z$ bosons. The measurements are compatible with the Standard Model expectation, with uncertainties between 30\% and 300\%. Limits are subsequently set on the parameters of an effective Lagrangian sensitive to modifications of the associated production of a Higgs boson. The combination provides more stringent limits than the individual analyses on parameters that depend strongly on the electroweak gauge boson's momentum.

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