Geomaterials, including sands, exhibit complex mechanical behaviour under loading, such as state and time dependence, anisotropy, stress-dilatancy and stress-path dependence. Recently data-driven machine learning (ML) methods have attracted significant interest as surrogate models for such behaviour. Most ML methods, however, rely on large, high-quality training datasets, which limits their applicability in sparse-data regimes. Moreover, despite recent progress in leveraging laboratory test data, relatively few studies explicitly bridge the traditional constitutive modelling and experimental observations within a unified framework. Transfer learning (TL) offers a flexible approach in which a pretrained model is reused as the starting point for a related task. In this work, we propose a model-informed transfer learning strategy using two approximators: a predictor, and a residual model. Both are implemented using artificial neural networks (ANN) to exploit their expressivity and automatic differentiation (AD) capability. The predictor ANN is trained with sparse data by minimising a loss function that embeds a traditional constitutive model, in a manner analogous to physics-informed neural network formulations. The predictor may include free constitutive model parameters, which can be inferred in an inverse-problem setting. The trained predictor is then utilised to train the residual ANN, which learns the discrepancy profile between the predictor and experimental data, thereby capturing model-data mismatch as well as measurement error. We demonstrate the versatility of the proposed framework using the constitutive model in [1] for model parameter learning and prediction of the triaxial behaviour of Toyoura sand [1] and Karlsruhe fine sand [2] for varying confining pressure, void ratio, and drainage conditions.