Quantum Computing (QC) along with Edge-Driven Intelligence (EDI) is becoming a powerful paradigm for decentralized decision-making and data processing driven by the explosive growth of Internet of Things (IoT) appliances and the massive growth of data generated at the network edge. However, there are also a lot of security, privacy, and trust-related issues that come with executing EDI. Some of the most pressing issues our world is facing could be resolved by quantum computing, include those related to materials science, energy, climate, agriculture, health, and the environment, etc. As the size of the system increases, classical computing becomes more difficult to solve some of these issues. Thus, considering the security, privacy, and trust in the context of QC and EDI, this abstract delves into the main problems and factors encountered in present era of technology. We address the particular risks to security such as data leaks, illegal access, and Denial-of-Service (DoS) attacks that are brought about by the distributed nature of edge computing environments. We have also discussed the privacy consequences of handling sensitive data at the edge including location and health data, and the importance of putting strong privacy-preserving measures in place. In order to create safe and reliable quantum-edge computing ecosystems, we have outlined the potential approaches and solutions for boosting security, protecting privacy, and building faith in the quickly changing field of edge-driven intelligence.