Differential cross-section measurements of Zγ production in association with hadronic jets are presented, using the full 139 fb ⁻¹ dataset of s = 13 TeV proton–proton collisions collected by the ATLAS detector during Run 2 of the LHC. Distributions are measured using events in which the Z boson decays leptonically and the photon is usually radiated from an initial-state quark. Measurements are made in both one and two observables, including those sensitive to the hard scattering in the event and others which probe additional soft and collinear radiation. Different Standard Model predictions, from both parton-shower Monte Carlo simulation and fixed-order QCD calculations, are compared with the measurements. In general, good agreement is observed between data and predictions from MATRIX and MiNNLO_PS, as well as next-to-leading-order predictions from MadGraph5_aMC@NLO and Sherpa. [Figure not available: see fulltext.]