Integrating Adaptive Mesh Refinement (AMR) into climate models is problematic partly because several components have difficulty in accommodating adaptive grids. However, on coarse resolutions, errors from each component of climate models contribute to the overall errors of the model output. Using AMR in single components should reduce the overall model error. Besides, we can use AMR in existing climate models with reduced development time compared to designing a new AMR model. We integrate AMR into the tracer transport module of the atmospheric model ECHAM6 and test our implementation in idealized scenarios as well as on a realistic application (dust transport). To achieve this goal, we modify the Flux-Form Semi-Lagrangian (FFSL) transport scheme in ECHAM6 such that we can use it on adaptive meshes while retaining all important properties such as mass conservation of the original implementation. Our proposed scheme is dimensionally split and ensures that high-resolution information is always propagated on (locally) highly resolved meshes. We introduce a data structure that can accommodate an adaptive grid. We demonstrate that our AMR scheme improves both accuracy and efficiency compared to the original scheme. More importantly, our approach improves the representation of transport processes in ECHAM6 for coarse resolution simulations. Hence, the results of this paper suggest that we can overcome the overhead of developing a fully adaptive earth system model by integrating AMR into single components while leaving data structures of the dynamical core untouched. This enables researches to retain well-tested legacy code of existing models while still improving accuracy.