Converging Zero Trust (ZT) with learning techniques can solve various operational and security challenges in Distributed Computing Continuum Systems (DCCS). Implementing centralized ZT architecture is seen as unsuitable for the computing continuum (e.g., computing entities with limited connectivity and visibility, etc.). At the same time, implementing decentralized ZT in the computing continuum requires understanding infrastructure limitations and novel approaches to enhance resource access management decisions. To overcome such challenges, we present a novel learning-driven ZT conceptual architecture designed for DCCS. We aim to enhance ZT architecture service quality by incorporating lightweight learning strategies such as Representation Learning (ReL) and distributing ZT components across the computing continuum. The ReL helps to improve the decision-making process by predicting threats or untrusted requests. Through an illustrative example, we show how the learning process detects and blocks the requests, enhances resource access control, and reduces network and computation overheads. Lastly, we discuss the conceptual architecture, processes, and provide a research agenda.