This paper studies how to develop accurate and interpretable time series classification (TSC) models with the help of external data in a privacy-preserving federated learning (FL) scenario. To the best of our knowledge, we are the first to study on this essential topic. Achieving this goal requires us to seamlessly integrate the techniques from multiple fields including Data Mining, Machine Learning, and Security. In this paper, we formulate the problem and identify the interpretability constraints under the FL setting. We systematically investigate existing TSC solutions for the centralized scenario and propose FedST, a novel FL-enabled TSC framework based on a shapelet transformation method. We recognize the federated shapelet search step as the kernel of FedST. Thus, we design $\Pi_{FedSS-B}$, a basic protocol for the FedST kernel that we prove to be secure and accurate. Further, we identify the efficiency bottlenecks of the basic protocol and propose optimizations tailored for the FL setting for acceleration. Our theoretical analysis shows that the proposed optimizations are secure and more efficient. We conduct extensive experiments using both synthetic and real-world datasets. Empirical results show that our FedST solution is effective in terms of TSC accuracy, and the proposed optimizations can achieve three orders of magnitude of speedup.