Peck has been at the agency for 11 years, most recently as head of medical education. As managing director she will oversee operations, advance business performance and provide strategic leadership, the agency said.
Her promotion follows several new account wins and hires for the agency this year.
Peck joins the board of the Communications Division at parent Unlimited Group, and will report to Communications Division chief executive Nick Clark. She will be supported by an eight-strong management team at Health Unlimited, which employs about 40 consultants.
Over a 15-year career, Peck has worked in a range of healthcare comms areas including oncology, dermatology, infectious diseases, immunology, gastroenterology and neurology.
Bradley departs in July after six years as managing director.
Unlimited Group chief executive Tim Hassett said: “I’m a big believer in world-class talent and that can be home-grown. This was a natural step in our eyes; Clare is highly respected by our clients from a strategic perspective and, as health remains a critically important sector for us, she’s the strong leader we need to take the helm. Clare joins the Communications board in a senior leadership position here at Unlimited, of which we are all extremely proud.”
Clark said: “As we look to create a more integrated offering across our b2b, consumer and health areas of expertise, Clare is uniquely positioned to lead the health team to deliver even more award-winning work for our clients and help drive our integrated ambitions.”
Peck said: “Our team comprises exceptional talent with broad-ranging capabilities and this is well-reflected in our strong and longstanding client relationships, some of which we have held for over 10 years. It’s an exciting, but clearly challenging, time for our sector.
"However, we continue supporting our clients' switch to virtual workshops and events, develop COVID-19-conscious communications and fast-track remote learning and stakeholder-engagement projects. We are showing business resilience, having won several new client accounts and welcomed five new team members this year.”