Cases of COVID-19 are escalating rapidly across the globe, with the mortality risk being especially high among those with existing illness and multimorbidity. This study aimed to synthesise evidence for the role and response of palliative care and hospice teams to viral epi/pandemics, to inform the COVID-19 pandemic response. We conducted a rapid systematic review according to PRISMA guidelines in five databases. Of 3094 papers identified, ten were included in this narrative synthesis. Included studies were from West Africa, Taiwan, Hong Kong, Singapore, the United States and Italy. All had an observational design. Findings were synthesised using a previously proposed framework according to ‘systems’ (policies, training and protocols, communication and coordination, data), ‘staff’ (deployment, skill mix, resilience), ‘space’ (community provision, use of technology) and ‘stuff’ (medicines and equipment, personal protective equipment). We conclude that hospice and palliative services have an essential role in the response to COVID-19 by: 1) responding rapidly and flexibly; 2) ensuring protocols for symptom management are available, and training non-specialists in their use; 3) being involved in triage; 4) considering shifting resources into the community; 5) considering redeploying volunteers to provide psychosocial and bereavement care; 6) facilitating camaraderie among staff and adopt measures to deal with stress; 7) using technology to communicate with patients and carers; 8) adopting standardised data collection systems to inform operational changes and improve care.