"I take that responsibility very seriously indeed and I expect our staff to work and act at all times with a level of professionalism that honours the trust our patients place in us."
Ms Claire said any breach of a patient's privacy was taken seriously and, if proved, would result in disciplinary action.
"ADHB has robust HR processes and any apparent breaches of privacy will be investigated and action taken where appropriate."
Ms Clair said board chairman Dr Lester Levy had "made it very clear that ... he will not tolerate this type of behaviour".
"He and I stand shoulder-to-shoulder on this issue.
"I have met our senior leaders and outlined my expectations very clearly.
"I have asked that my expectations be reinforced with staff."
The Herald on Sunday reported a hospital source as saying the eel was "about the size of a decent sprig of asparagus".
"The incident is the talk of the place. Doctors and nurses have come across people with strange objects that have got stuck where they shouldn't be before, but an eel has to be a first," the source was reported as saying.
At the time, ADHB spokesman Matt Rogers confirmed a man had "presented at Auckland City Hospital ... with an eel inside him".