Purpose: Higher education and its leadership are not yet using their potential impact for a sustainable future. This paper aims to focus on UN developments and the long history of university involvement in sustainability might create more interest and understanding that sustainably oriented universities are actually possible and a much stronger role for higher education is needed when nations are discussing their future. Design/methodology/approach: Literature review with a focus on international treaties and declarations on the UN level and international university networks, literature review of the background and potential of the whole-institution approach and the need/suggestions for further research, also to measure advancement. Findings: History shows a strong engagement of higher education with sustainability from its beginnings. There have been strong calls/offers from within university networks to take a crucial role in moving towards sustainable development that involves more than teaching about sustainability. The international community calls for higher education to be involved in policymaking rather than simply implementation, have been limited and the full potential of higher education institutions using all opportunities such as being living labs for sustainability has not as yet been realized. Currently, calls for engagement are often still limited to training and providing research when scientific evidence is wanted. Research limitations/implications: Literature review focused on UN level treaties/declarations English- and German-language review national developments limited to samples of members of the Sustainable Development Goal (SDG) 4 subcluster in the Higher Education and Research for Sustainable Development (HESD) Global Cluster by the International Association of Universities (IAU). Practical implications: Guidance for university leaders and other stakeholders to become aware of and consider a whole-institution approach. Practitioner relevance as countries is encouraged to embed UN recommendations, treaties and declarations. Defining opportunities for further research. Presenting the HESD Cluster by the IAU as a sample for new approaches of higher education to interact with the SDGs. Social implications: Strengthening the role of higher education in the pursuit of a better future would focus on science and research as a neutral basis for decision-making and policy development. Sustainability embedded in all streams of university can help universities to be a practical example of the possibilities of sustainability at work. Originality/value: Composition of authors with UN background and involvement. Focus on UN treaties/declarations and guidance for academics and practitioners in leadership on adopted UN and other international documents. Summarizing the background of the whole-institution approach as a genuine development over time but including limitations and implications for future roles for higher education leadership. IAU SDG 4 Subcluster is unique in its own approach and with its connections to a global network of higher education institutions and UNESCO.