Student agency is a key educational goal increasingly being impacted by Artificial Intelligence (AI) systems integrated into the human learning process. In September 2023, the Ministers responsible for education decided to develop two policy instruments to regulate AI in education, setting teacher and learner agency as a policy goal. To examine how agency for AI regulation in the Europe is understood in policy discourse, I conducted an inductive content analysis of the documents that serve as a basis for these policy instruments. Using documents referred to in Resolution Three on Harnessing the Potential for AI in and through Education as the basis for analysis, five main areas of agency implementation were identified: ethics, AI literacy, regulations, pedagogy, and the capacity to exercise rights and attributes within each field. Key findings, three strains for agency, can guide policy makers and educational practitioners to define actors' roles and responsibility when using AI in the classroom. Different areas of implementation and attributes of agency exist, which will likely guide decision-making and design of policy instruments to assess and ensure agency when AI is employed in an educational context.