Many real-world applications such as robotics provide hard constraints on power and compute that limit the viable model complexity of Reinforcement Learning (RL) agents. Similarly, in many distributed RL settings, acting is done on un-accelerated hardware such as CPUs, which likewise restricts model size to prevent intractable experiment run times. These "actor-latency" constrained settings present a major obstruction to the scaling up of model complexity that has recently been extremely successful in supervised learning. To be able to utilize large model capacity while still operating within the limits imposed by the system during acting, we develop an "Actor-Learner Distillation" (ALD) procedure that leverages a continual form of distillation that transfers learning progress from a large capacity learner model to a small capacity actor model. As a case study, we develop this procedure in the context of partially-observable environments, where transformer models have had large improvements over LSTMs recently, at the cost of significantly higher computational complexity. With transformer models as the learner and LSTMs as the actor, we demonstrate in several challenging memory environments that using Actor-Learner Distillation largely recovers the clear sample-efficiency gains of the transformer learner model while maintaining the fast inference and reduced total training time of the LSTM actor model.