Quantum Materials represent a frontier research endeavour. The strong interactions at the heart of their exotic physical properties has made understanding, let alone predicting, their materials properties one of the most profound challenges of modern-day solid state physics and materials chemistry. This problem is not just an intellectual curiosity, however; harnessing control over the collective states that these systems can host, such as superconductivity, metal-insulator transitions, and magnetic orderings, could open new routes to designing fast, energy-efficient, and smart multifunctional technologies, operating using completely different design principles to the Silicon-based logic of today. To progress towards an improved fundamental understanding, and thereby ultimate exploitation, of these systems requires controlled, new, experimental approaches. Here, we propose to develop new capabilities for applying large, reversible, and continuously-tuneable uniaxial pressures in conjunction with angle-resolved photoemission experiments. This promises novel insight into how the electronic structures and many-body interactions of quantum materials evolve when subjected to a particularly clean tuning parameter, which is of fundamental importance to further our understanding of the quantum many-body problem in solids. To this end, we will focus on two key materials systems, the metallic transition-metal dichalcogenides and the layered ruthenate oxides. These are each of enormous current interest in their own right, as potential hosts of topological excitations, as new 2D materials candidates, and as unconventional magnets, and are chosen here to provide important complementary insights into the nature of phase competition, electron-lattice interactions, and strong electronic correlations in solids.