Universities are increasingly adopting data-driven strategies to enhance student success, with AI applications like Learning Analytics (LA) and Predictive Learning Analytics (PLA) playing a key role in identifying at-risk students, personalising learning, supporting teachers, and guiding educational decision-making. However, concerns are rising about potential harms these systems may pose, such as algorithmic biases leading to unequal support for minority students. While many have explored the need for Responsible AI in LA, existing works often lack practical guidance for how institutions can operationalise these principles. In this paper, we propose a novel Responsible AI framework tailored specifically to LA in Higher Education (HE). We started by mapping 11 established Responsible AI frameworks, including those by leading tech companies, to the context of LA in HE. This led to the identification of seven key principles such as transparency, fairness, and accountability. We then conducted a systematic review of the literature to understand how these principles have been applied in practice. Drawing from these findings, we present a novel framework that offers practical guidance to HE institutions and is designed to evolve with community input, ensuring its relevance as LA systems continue to develop.