Pansharpening is a critical yet challenging low-level vision task that aims to obtain a higher-resolution image by fusing a multispectral (MS) image and a panchromatic (PAN) image. While most pansharpening methods are based on convolutional neural network (CNN) architectures with standard convolution operations, few attempts have been made with context-adaptive/dynamic convolution, which delivers impressive results on high-level vision tasks. In this paper, we propose a novel strategy to generate local-context adaptive (LCA) convolution kernels and introduce a new global harmonic (GH) bias mechanism, exploiting image local specificity as well as integrating global information, dubbed LAGConv. The proposed LAGConv can replace the standard convolution that is context-agnostic to fully perceive the particularity of each pixel for the task of remote sensing pansharpening. Furthermore, by applying the LAGConv, we provide an image fusion network architecture, which is more effective than conventional CNN-based pansharpening approaches. The superiority of the proposed method is demonstrated by extensive experiments implemented on a wide range of datasets compared with state-of-the-art pansharpening methods. Besides, more discussions testify that the proposed LAGConv outperforms recent adaptive convolution techniques for pansharpening.