The COVID-19 health crisis has caused profound social and economic disruptions. Affecting everyone, its impact is not equal. Exacerbating deep social fissures and long-standing systemic inequalities, the pandemic reveals the fragilities and inequities in global higher education. Accelerating underlying trends and triggering seismic shifts in the sector, collective efforts over a period of weeks delivered massive change in a sector not known for being fleet-of-foot. As we envisage the ‘next normal’ for higher education, problems with the ‘old normal’ may be fixed and some recent innovations carried forward. Representing a period of punctuated equilibrium, COVID-19 could lead to transformation of the sector towards greater equity and impact across teaching/learning, research/innovation, community service/engagement and the staff/students’ experience. As we ask, “When will HE open again?”, and “When we do, what will it be like?” we may also find ourselves considering “Will some institutions open at all?” Seeking to navigate these volatile, uncertain, complex and ambiguous times—so-called VUCA conditions—we propose that the SDGs are positioned as a lens to re-imagine higher education in mounting an antifragility response. We examine whether a new paradigm is forming that could be more sustainable as budgets, priorities and institutional archetypes are challenged fundamentally in line with delivery against the SDGs.