Scientific research organizations that are developing and deploying Artificial Intelligence (AI) systems are at the intersection of technological progress and ethical considerations. The push for Responsible AI (RAI) in such institutions underscores the increasing emphasis on integrating ethical considerations within AI design and development, championing core values like fairness, accountability, and transparency. For scientific research organizations, prioritizing these practices is paramount not just for mitigating biases and ensuring inclusivity, but also for fostering trust in AI systems among both users and broader stakeholders. In this paper, we explore the practices at a research organization concerning RAI practices, aiming to assess the awareness and preparedness regarding the ethical risks inherent in AI design and development. We have adopted a mixed-method research approach, utilising a comprehensive survey combined with follow-up in-depth interviews with selected participants from AI-related projects. Our results have revealed certain knowledge gaps concerning ethical, responsible, and inclusive AI, with limitations in awareness of the available AI ethics frameworks. This revealed an overarching underestimation of the ethical risks that AI technologies can present, especially when implemented without proper guidelines and governance. Our findings reveal the need for a holistic and multi-tiered strategy to uplift capabilities and better support science research teams for responsible, ethical, and inclusive AI development and deployment.