The account will be led from Fleishman's Dublin office, the site of one of its new client's main operational hubs.
The Omnicom-owned agency took over the brief from Grayling in November. The latter confirmed it had held the account for the past five years.
Fleishman's contract does not have a set end date, a spokeswoman for the firm said.
Orla Burke, EMEA healthcare lead at the agency said: "It’s an interesting time to work in the healthcare sector with lots of challenges and Allianz Worldwide Care provides solutions that make a real impact for organisations, individuals and partners. I’m looking forward to bringing our expertise in health, insurance, retail and technology to bear while supporting the team at Allianz Worldwide Care."
Allianz Worldwide Care is a specialist brand of the broader Allianz Worldwide Partners, which has a total of 16,000 employees across 35 countries.