As telecommunications technology progresses, telehealth frameworks are becoming more widely adopted in the context of long-term care (LTC) for older adults, both in care facilities and in homes. Today, robots could assist healthcare workers when they provide care to elderly patients, who constitute a particularly vulnerable population during the COVID-19 pandemic. Previous work on user-centered design of assistive technologies in LTC facilities for seniors has identified positive impacts. The need to deal with the effects of the COVID-19 pandemic emphasizes the benefits of this approach, but also highlights some new challenges for which robots could be interesting solutions to be deployed in LTC facilities. This requires customization of telecommunication and audio/video/data processing to address specific clinical requirements and needs. This paper presents OpenTera, an open source telehealth framework, aiming to facilitate prototyping of such solutions by software and robotic designers. Designed as a microservice-oriented platform, OpenTera is an end-to-end solution that employs a series of independent modules for tasks such as data and session management, telehealth, daily assistive tasks/actions, together with smart devices and environments, all connected through the framework. After explaining the framework, we illustrate how OpenTera can be used to implement robotic solutions for different applications identified in LTC facilities and homes, and we describe how we plan to validate them through field trials.