3D Gaussian Splatting (3DGS) is a prevailing technique to reconstruct large-scale 3D scenes from multiview images for novel view synthesis, like a room, a block, and even a city. Such large-scale scenes are not static with changes constantly happening in these scenes, like a new building being built or a new decoration being set up. To keep the reconstructed 3D Gaussian fields up-to-date, a naive way is to reconstruct the whole scene after changing, which is extremely costly and inefficient. In this paper, we propose a new method called GauUpdate that allows partially updating an old 3D Gaussian field with new objects from a new 3D Gaussian field. However, simply inserting the new objects leads to inconsistent appearances because the old and new Gaussian fields may have different lighting environments from each other. GauUpdate addresses this problem by applying inverse rendering techniques in the 3DGS to recover both the materials and environmental lights. Based on the materials and lighting, we relight the new objects in the old 3D Gaussian field for consistent global illumination. For an accurate estimation of the materials and lighting, we put additional constraints on the materials and lighting conditions, that these two fields share the same materials but different environment lights, to improve their qualities. We conduct experiments on both synthetic scenes and real-world scenes to evaluate GauUpdate, which demonstrate that GauUpdate achieves realistic object insertion in 3D Gaussian fields with consistent appearances.