The CMS Collaboration has reported new results on the Central Exclusive Production (CEP), $pp \to p\oplus X\oplus p$, using data collected from 2016 to 2018. These results explore precise measurements of the electroweak sector of the Standard Model and searches for potential signs of New Physics. The continuation of this program has been outlined in an Expression of Interest, proposing further study of CEP events at the High-Luminosity Large Hadron Collider (HL-LHC) with detection of very forward protons. In this document, we present key aspects related to the expected detector performance and the outlook for physics studies to be conducted using the near-beam proton spectrometer at the HL-LHC.