  We analyze the scenario within the Next to Minimal Supersymmetric Standard
Model (NMSSM), where the lightest supersymmetric particle (LSP) is
singlino-like neutralino. By systematically considering various possible
admixtures in the electroweakino sector, we classify regions of parameter space
where the next to lightest supersymmetric particle (NLSP) is a long-lived
electroweakino while remaining consistent with constraints from flavor physics,
dark matter direct detection, and collider data. We identify viable cascade
decay modes featuring the long-lived NLSP for directly produced
chargino-neutralino pairs, thus, leading to displaced vertex signatures at the
high luminosity LHC (HL-LHC). We construct track based analysis in order to
uncover such scenarios at the HL-LHC and analyze their discovery potential. We
show that through such focused searches for the long-lived particles at the
HL-LHC, one can probe regions of the electroweakino parameter space that are
otherwise challenging.
