The Future Circular electron-positron Collider (FCC-ee) is a high luminosity frontier particle accelerator for high precision measurements of the heaviest fundamental particles and possible evidence of new physics. Heavy Neutral Leptons (HNLs) are examples of new particles with discovery potential at the FCC-ee that could answer some of the most substantial questions in particle physics, such as how neutrinos oscillate between flavour eigenstates. Their estimated discovery region at the FCC-ee includes masses and mixing angles that allow the HNLs to attain long-lived properties. Therefore, long-lived signatures such as displaced vertices can be considered in this search for these particles. This thesis presents the first sensitivity analysis of these long-lived HNLs in the FCC-ee framework for the experimental run at the Z pole. The signal simulation used the Type I Seesaw mechanism with one benchmark HNL mixing with electron flavours and leptonic final states with electrons and electron neutrinos. An analysis of the signal and background is given, which results in a proposed event selection to reduce the background and increase the signal sensitivity. The final results include a sensitivity plot as a function of mass and mixing angle. This first successful implementation of a HNL analysis in future colliders can be used as a foundation for future explorations of long-lived HNLs at FCC-ee.