Understanding how climate change will affect oceanic fluid transport is crucial for environmental applications and human activities. However, a synoptic characterization of the influence of climate change on mesoscale stirring and transport in the surface ocean is missing. To bridge this gap, we exploit a high-resolution, fully coupled climate model of the Mediterranean basin using a Network Theory approach. We project significant increases of horizontal stirring and kinetic energies in the next century, likely due to increments of available potential energy. The future evolution of basin-scale transport patterns hints at a rearrangement of the main hydrodynamic provinces, defined as regions of the surface ocean that are well mixed internally but with minimal cross-flow across their boundaries. This results in increased heterogeneity of province sizes and stronger mixing in their interiors. Our approach can be readily applied to other oceanic regions, providing information for the present and future marine spatial planning. Plain Language Summary Transport and mixing of water masses driven by ocean currents influence a variety of fundamental processes, including heat redistribution, ecosystem functioning, and pollutants spreading. Therefore, understanding how fluid transport will be affected by climate change is crucial, in particular in the ocean surface, where marine life and human activities are concentrated. Here, we exploit a state-of-the-art climate model over the Mediterranean basin using a novel methodology which integrates Network Theory concepts with Lagrangian modeling. We assess past conditions and future changes at climatic scales of ocean stirring and transport over the entire basin. Our results reveal a significant increment of surface stirring linked to an increase of currents kinetic energy, which in turn could be ascribed to increments of available potential energy. We then provide a regionalization of the ocean surface based on hydrodynamic provinces that are well mixed internally but with little leaking across their boundaries. Our model project an increased heterogeneity of province sizes and a stronger mixing in their interiors, while their mean area and coherence remain unaffected. Our approach could be applied to other oceanic domains and help designing adaptive strategies for marine spatial planning.