This narrative inquiry explores three Chinese university leaders' intercultural competence as a key dimension of their leadership that overseas leadership development programmes enabled them to develop. The leaders visited three different countries -- namely, the United States, the United Kingdom and Canada -- storied their experiences in the programmes and connected their reflections to leadership in the Chinese higher education system. Our narrative analyses show that the overseas leadership development programmes were mediators in the construction of leadership, for which there were two focal themes: (1) leadership as a personal and contextual construction process and (2) intercultural competence as a key dimension of university leaders' leadership. Betwixt and between different higher education systems in different cultural contexts, the reconceptualisation of leadership with intercultural competence is unfurled in the liminal space, which goes beyond the functionalist paradigm of leadership and is also of international interest and value in the global communication of higher education.