We demonstrate the first climate-scale, numerical ocean simulations improved through distributed, online inference of Deep Neural Networks (DNN) using SmartSim. SmartSim is a library dedicated to enabling online analysis and Machine Learning (ML) for traditional HPC simulations. In this paper, we detail the SmartSim architecture and provide benchmarks including online inference with a shared ML model on heterogeneous HPC systems. We demonstrate the capability of SmartSim by using it to run a 12-member ensemble of global-scale, high-resolution ocean simulations, each spanning 19 compute nodes, all communicating with the same ML architecture at each simulation timestep. In total, 970 billion inferences are collectively served by running the ensemble for a total of 120 simulated years. Finally, we show our solution is stable over the full duration of the model integrations, and that the inclusion of machine learning has minimal impact on the simulation runtimes.