Young and middle-aged pulsars are well-known emitters of gamma rays in the TeV range. Many of the unidentified sources detected by the Large High Altitude Air Shower Observato- ry (LHAASO), down to energies in the PeV range, appear to be associated with pulsars or pulsar wind nebulae. However, there is little evidence of TeV emission from millisecond pulsars (MSPs). While the GeV emission from MSPs comes mainly from curvature radiation, the TeV emission is more likely to be linked to secondary processes involving particles escaping from the magnetosphere. The aim of this project is to explore theoretical models of the secondary TeV emission from MSPs. Using advanced simulations of pulsar particle emission, we will seek to understand how environmental conditions influence the final photon spectrum. The main objective is to estimate the cumulative TeV emission from Galactic MSPs and to identify unique spectral or morphological signatures that could guide future observational searches.