The LHCb RICH detector will undergo a significant upgrade during LS3 as part of an approved enhancement program to introduce fast-timing information. The upgrade will address the challenges posed by increased particle multiplicity and high occupancy anticipated for the LHC HL phase. Integrating sub-100 ps timing information is crucial for maintaining excellent particle identification (PID) performance. In the RICH detector, Cherenkov photons from a track arrive nearly simultaneously at the detector plane, allowing precise hit time prediction. Determining the primary vertex time (PV T$_0$) is key to accurately predicting the time of arrival of photons on the photodetector plane. By integrating time information in the RICH reconstruction, a software time gate can be applied around the predicted time per track to enhance signal-to-background ratio and PID performance. This contribution describes the integration of fast-timing information into the RICH detector, focusing on a novel method to estimate PV T$_0$ using only RICH information.