Hypervisors are increasingly complex and must be often updated for applying security patches, bug fixes, and feature upgrades. However, in a virtualized cloud infrastructure, updates to an operational hypervisor can be highly disruptive. Before being updated, virtual machines (VMs) running on a hypervisor must be either migrated away or shut down, resulting in downtime, performance loss, and network overhead. We present a new technique, called HyperFresh, to transparently replace a hypervisor with a new updated instance without disrupting any running VMs. A thin shim layer, called the hyperplexor, performs live hypervisor replacement by remapping guest memory to a new updated hypervisor on the same machine. The hyperplexor leverages nested virtualization for hypervisor replacement while minimizing nesting overheads during normal execution. We present a prototype implementation of the hyperplexor on the KVM/QEMU platform that can perform live hypervisor replacement within 10ms. We also demonstrate how a hyperplexor-based approach can used for sub-second relocation of containers for live OS replacement.