Large Language Models such as ChatGPT have caused a disruptive storm by applying AI in various fields, including education. This has led to discussions on its use and implications. Some educational institutions rapidly developed policies or guidelines to restrict its use. At the same time, others began to experiment with ways in which it could be used to support teaching and learning. There are opportunities and challenges, which the ADMIT cooperation partnership decided to explore with an eye on future developments, that would enable universities to improve higher education. The overarching project objective is then to establish the necessary educational and ethical conditions that enable the utilization of LLM and generative AI as a means of enhancing teaching and learning in higher education. A LLM-ed framework and guidelines, using Large Language Models for education, will be created for integrating LLM and generative AI into teaching and learning design. The outcomes of the project provide support for all stakeholders involved in their key roles and responsibilities: students, teachers, teaching and learning and IT support services, institutional leadership, and national and EU authorities. For building the LLM-ed framework and guidelines, the ADMIT project will continuously track the latest developments in research, innovation, and institutional policies and strategies related to LLM and on evolving practices and policies in the partnership during the whole project lifetime. It will also develop recommendations and guidelines for the ethical use of LLM and generative LLM for teachers and students, including institutional recommendations. Finally, it will develop online course modules for the continuing professional development of staff and leadership European-wide on the use of LLM and generative AI in higher education.