A search for an exotic decay of the Higgs boson to a Z boson and a light pseudoscalar particle (a), decaying to a pair of leptons and a pair of photons, respectively, is presented. The search is based on proton-proton collision data at a center-of-mass energy of s=13TeV, collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 138fb−1. The analysis probes pseudoscalar masses ma between 1 and 30 GeV, leading to two pairs of well-isolated leptons and photons. Upper limits at 95% confidence level are set on the Higgs boson production cross section times its branching fraction to two leptons and two photons. The observed (expected) limits are in the range of 1.1–17.8 (1.7–17.9) fb within the probed ma interval. An excess of data above the expected standard model background with a local (global) significance of 2.6 (1.3) standard deviations is observed for a mass hypothesis of ma=3GeV. Limits on models involving axion-like particles, formulated as an effective field theory, are also reported.