The Trust said it has taken additional measures to ensure it can continue to deliver a service to the public.
Head of Service at the Trust, Stephen Sheldon, said the public can help by only calling 999 in the event of a life-threatening emergency.
“That’s a cardiac arrest, chest pain or breathing difficulties, loss of consciousness, choking, or catastrophic bleeding,” Mr Sheldon added.
The service is advising the public to visit the NHS 111 Wales website for health advice or to consult a GP, pharmacist, and minor injuries unit.