The report focuses on the problem of continuity between preschool and primary education in developing a child’s competences. Modern approaches to solving the outlined issue in research and educational practices are characterised. An analysis of the content of regulatory documents, particularly the state standards of preschool and primary education, is presented to identify common approaches, values, principles, and cross-cutting competences in children’s development. It was found that for development of a competent personality in preschool and primary school age is essential not only balanced content of regulations of the mentioned levels, but also awareness of teachers and parents of the child’s age peculiarities, joint approach in selecting methods, forms, and means of educational work. The results of the research of modern practice of preschool education institutions on ensuring continuity and establishing a partnership with the primary school are given. Educators solve the problem of continuity by getting acquainted with the content of the New Ukrainian School programmes, using modern pedagogical technologies, educational work among parents, and cooperation with primary school teachers. Several organizational and pedagogical conditions are outlined, under which the continuity between preschool and primary education will be practically ensured.