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The hard X-ray emission from magnetars and other isolated neutron stars remains under-explored. An instrument with higher sensitivity to hard X-rays is critical to understanding the physics of neutron star magnetospheres and also the relationship between magnetars and Fast Radio Bursts (FRBs). High sensitivity to hard X-rays is required to determine the number of magnetars with hard X-ray tails, and to track transient non-thermal emission from these sources for years post-outburst. This sensitivity would also enable previously impossible studies of the faint non-thermal emission from middle-aged rotation-powered pulsars (RPPs), and detailed phase-resolved spectroscopic studies of younger, bright RPPs. The High Energy X-ray Probe (HEX-P) is a probe-class mission concept that will combine high spatial resolution X-ray imaging (<5 arcsec half-power diameter (HPD) at 0.2–25 keV) and broad spectral coverage (0.2–80 keV) with a sensitivity superior to current facilities (including XMM-Newton and NuSTAR). HEX-P has the required timing resolution to perform follow-up observations of sources identified by other facilities and positively identify candidate pulsating neutron stars. Here we discuss how HEX-P is ideally suited to address important questions about the physics of magnetars and other isolated neutron stars.