Eluned was appointed Minister for Health and Social Services on 13 May 2021, and re-appointed as Cabinet Secretary for Health and Social Care on 21 March 2024.
Penodwyd Eluned yn Weinidog Iechyd a Gwasanaethau Cymdeithasol ar 13 Mai 2021, a cafodd ei hailbenodi yn Ysgrifennydd y Cabinet dros Iechyd a Gofal Cymdeithasol ar 21 Mawrth 2024.