The design of prompt-gamma detectors necessitates numerous Monte Carlo simulations to precisely develop and optimize the detection stages in proton therapy. Alongside the advancement of MC simulations, various variance reduction methods have been explored to speed-up calculations. Among these techniques, track-length estimators are interesting scoring methods for achieving both speed and accuracy in Monte Carlo simulations of rare events. This paper introduces an extension of the GATE vpgTLE module that incorporates the prompt-gamma emission time, which is tagged from the proton tracking, enhancing its utility for studies focused on detector design and optimization that rely on time measurements. The results obtained from a clinical radiotherapy plan are presented. We demonstrate that the new vpgTLE tally with time tagging is accurate, except for certain prompt-gamma lines corresponding to long mean-life nuclei.