We present a hybrid MPI-OpenMP implementation of Linear-Scaling Density Functional Theory within the ONETEP code. We illustrate its performance on a range of high performance computing (HPC) platforms comprising shared-memory nodes with fast interconnect.Our work has focused on applying OpenMP parallelism to the routines which dominate the computational load, attempting where possible to parallelise different loops from those already parallelised within MPI. This includes 3D FFT box operations, sparse matrix algebra operations, calculation of integrals, and Ewald summation. Whilst the underlying numerical methods are unchanged, these developments represent significant changes to the algorithms used within ONETEP to distribute the workload across CPU cores. The new hybrid code exhibits much-improved strong scaling relative to the MPI-only code, and permits calculations with a much higher ratio of cores to atoms. These developments result in a significantly shorter time to solution than was possible using MPI alone, and facilitate the application of the ONETEP code to systems larger than previously feasible. We illustrate this with benchmark calculations from an amyloid fibril trimer containing 41,907 atoms. We use the code to * To whom correspondence should be addressed † School of Chemistry, University of Southampton, Southampton, SO17 1BJ, UK ‡ TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom 1 study the mechanism of delamination of cellulose nano-fibrils when undergoing sonification, a process which is controlled by a large number of interactions that collectively determine the structural properties of the fibrils. Many energy evaluations were needed for these simulations and as these systems comprise up to 21,276 atoms this would not have been feasible without the developments described here.