Increasing demand for secure remote operation in industry and technology advancements to support delivering efficient services and tele-mentoring have opened a new market in healthcare sector and emergency services based on 5G and Tactile internet capabilities. In a connected world, hospitals would benefit from providing the on-time availability either for continuous health monitoring or critical services to the citizens in need. In this paper, we propose a Secure Non-Public Health Enterprise Network concept to enable an end-to-end secure and location-agnostic communication between a patient and a healthcare service provider, and other contacts with patient's consent either in case of an emergency or to be stored in the medical records. We present how applying non-public enterprise networks can address market demand in health care sector for improved end-to-end security and privacy when dealing with personal and critical information. We present the three-tier architecture model describing continuous authentication mechanisms based on biometric collection as well as the dynamic network solutions in the healthcare domain. The biometric collection can be done using ambient/IoT sensors as well as wearable/implantable devices to monitor the patient unobtrusively. Furthermore, end-to-end security solutions based on the user profile and situation awareness to set and adapt the required level of security at the network side. We discuss the related research challenges for developing the proposed non-public health enterprise platform and provide suggestions for future work based on the healthcare sector requirements and opportunities.