The resolution and accuracy of numerical partial differential equation solvers are governed by the mesh density and the order of accuracy of the solver. Anisotropic mesh adaptation combined with a posteriori error estimation is known to be a powerful tool to enhance the efficiency of the solvers. However, in engineering applications involving multiple complex congurations, optimization or uncertainty quantication, generating a single adapted mesh to efficiently capture features of the solutions for all possible choices of the problem parameters (geometry, boundary conditions, etc.) is not feasible. This is particularly true when the solution is very sensitive to the problem parameters and changes in the topology of the solution features (e.g. one vs two shocks) occur for small changes in the computational setting. This paper presents a novel algorithm coupling partitioning the parameter space for efficient parameter clustering and local model order reduction and anisotropic mesh adaptation. The hierarchical partitioning is performed by sampling the parameter space using a full-order model on a relatively coarse mesh. The variance of the physical solutions is reconstructed in the parameter space using proper orthogonal decomposition and Taylor's series to guide each partition's size and shape. Subsequently, the solutions are sampled within the optimal partitions to compute the locally adapted mesh and optimal reduced-order model for each partition. The efficacy of the new algorithm is demonstrated by solving heat conduction with material discontinuity and compressible flow problems.