The European Union Artificial Intelligence Act (EU AI Act) introduces binding requirements for robustness, security, and accountability in high-risk AI systems. In practice, these requirements often conflict with data protection obligations under the General Data Protection Regulation (GDPR), where security mechanisms depend on access to sensitive data restricted by privacy regulations. This creates a “compliance trilemma” where making systems secured, protecting privacy, and being transparent can conflict with each other. Instead of treating this as purely a legal issue, as it is often approached in regulations and standards, this paper looks at it as a security engineering challenge. In real world use cases, these requirements behave like interconnected security services: some support each other, while others create conflicts and constraints. As a result, organizations can face situations where meeting one requirement makes it harder to satisfy another, leading to design-time compliance challenges. To address this challenge, this work proposes a dependency based security governance framework that explicitly accounts for dependencies between requirements. It combines dependency modeling with the Analytic Hierarchy Process (AHP) to support structured and transparent decision making. This allows conflicting requirements to be identified and systematically prioritized based on their relative importance. The approach is demonstrated through a financial fraud detection use case, illustrating how such conflicts can be managed in a practical and defensible manner.