Recently, the adoption of zero-trust security model and architecture has accelerated due to a number of factors such as prevalent usage of off-premises cloud technologies, diversity of IT devices and diffusion of IoT (Internet of Things). The model is based on concepts of multiple layers of trust and verification for users, devices, applications, and networks that are always assumed to be untrusted. High performance computing (HPC) has unique architectural aspects when it comes to applications, systems, networks, and data access, to deliver close-to-metal performance and to achieve scalability. Increasingly however, scientific workflows require end-to-end access to distributed resources, from edge to cloud to HPC and supercomputing systems. In this talk, I present defining characteristics of HPC applications and systems, and discuss key challenges in adopting a zero-trust security model within HPC ecosystems. I will highlight ongoing activities that can bridge gaps and identify topics for future development work.