High temperature superconductors, especially rare-earth barium copper oxide (REBa₂Cu₃O₇₋ₓ or REBCO) tapes are an enabling technology for magnetic fields beyond 23.5 T, the limit of the existing technology based on the low temperature superconductors (LTS) niobium–titanium (NbTi) and niobium–tin (Nb₃Sn). Due to their higher prices, REBCO tapes are in general only employed as insert coils in an LTS outsert. Due to the tape geometry, the effect of the screening currents is high in REBCO insert coils. The resulting screening current-induced field (SCIF) can distort the shape and magnitude as well as affect the temporal stability of the field after charging. Their influence has to be well understood and it can be a limiting factor in field quality critical applications such as nuclear magnetic resonance magnets. In this work, we present the test results of a layer-wound 4 T REBCO insert coil operated in the background of a 21 T LTS outsert reaching a combined field of 25 T. Using an array of 13 calibrated Hall sensors, we investigate the spatial and temporal effects of the SCIFs at different background fields. Series expansion is employed to separate the contributions of the insert and of the outsert. We present in this work the characterization of the effect of the SCIF on the shape of the field and on its temporal stability in background fields from 0 T up to 19 T. We compare the experimental results with existing simulation models for the validation of the model at high magnetic fields, which had never been done for layer-wound REBCO coils. Based on the experimental data, we demonstrate the necessity of SCIF-aware simulations for REBCO insert coils, regardless of the insert's relative operating current. Before summarizing and concluding the work, we give a short overview of proposed methods for SCIF reduction in REBCO coils from the literature.