As high-intensity short-pulse lasers that can operate at high-repetition-rate (HRR) (>10 Hz) come online around the world, the high energy density (HED) science they enable will experience a radical paradigm shift. The >103 increase in shot rate over today's shot-per-hour drivers translates into dramatically faster data acquisition, more experiments, and the ability to exploit machine learning, and thus the potential to significantly accelerate the advancement of HED science. A wide range of HED experiments, from opacity investigations to secondary source generation to plasma nuclear physics, will benefit from the increased statistics, precision, and exploration of phase space. Besides increasing the rate at which scientific experiments can be performed, HRR also allows for the rapid delivery of optimal experiments supported by simulations and modeling augmented by close coupling to empirical data. To fully realize such an HRR framework, numerous subsystems must be developed and brought together, including feedback laser control loops, high-throughput targetry and diagnostics, cognitive simulation, enhanced HED codes, and advanced data analytics. This paper describes the vision for an integrated HRR laser experimental HED system and outlines some of the major considerations and challenges for realizing it.