In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022$-$2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 fb$^{-1}$.