From a legal perspective, the advance health directive, should be legally sufficient for a health care provider to transmit your personal health information to your health care agent. Therefore as far as the health care directive is concerned no formal HIPAA release is required. However, there is a practical problem that the health care provider may not know what is and what is not legally sufficient. To be sure it is therefore advisable to also have an additional HIPAA release for the designated health care agent.
A durable power of attorney for finances or a living trust document usually does not contain an implied HIPAA release either. Nevertheless the designated agent or successor trustee might have to get access to your health information in order to diligently manage your finances. Therefore it is a good idea to expressively empower your trusted person to access your health information in accordance with HIPAA.