Large Language Models (LLMs) have shown impressive potential in clinical question answering (QA), with Retrieval Augmented Generation (RAG) emerging as a leading approach for ensuring the factual accuracy of model responses. However, current automated RAG metrics perform poorly in clinical and conversational use cases. Using clinical human evaluations of responses is expensive, unscalable, and not conducive to the continuous iterative development of RAG systems. To address these challenges, we introduce ASTRID - an Automated and Scalable TRIaD for evaluating clinical QA systems leveraging RAG - consisting of three metrics: Context Relevance (CR), Refusal Accuracy (RA), and Conversational Faithfulness (CF). Our novel evaluation metric, CF, is designed to better capture the faithfulness of a model's response to the knowledge base without penalising conversational elements. To validate our triad, we curate a dataset of over 200 real-world patient questions posed to an LLM-based QA agent during surgical follow-up for cataract surgery - the highest volume operation in the world - augmented with clinician-selected questions for emergency, clinical, and non-clinical out-of-domain scenarios. We demonstrate that CF can predict human ratings of faithfulness better than existing definitions for conversational use cases. Furthermore, we show that evaluation using our triad consisting of CF, RA, and CR exhibits alignment with clinician assessment for inappropriate, harmful, or unhelpful responses. Finally, using nine different LLMs, we demonstrate that the three metrics can closely agree with human evaluations, highlighting the potential of these metrics for use in LLM-driven automated evaluation pipelines. We also publish the prompts and datasets for these experiments, providing valuable resources for further research and development.