The dominant mechanisms underlying high-energy $\gamma$-ray emission from galaxies vary by galaxy type. In starbursts, a major contribution comes from neutral pion decay. This is driven by interactions between interstellar gas and hadronic cosmic rays (CRs), which are accelerated in strong shocks associated star formation activity and stellar remnants. Leptonic $\gamma$-ray emission can also arise from electrons directly energized in interstellar shocks, produced via charged pion decays, or emitted by pulsars and their surrounding halos. In quiescent galaxies, pulsars and their halos can represent a major $\gamma$-ray source class, with millisecond pulsars predominantly located in globular clusters (GCs) being particularly important. Recent detections of very high-energy (VHE) emission from Galactic GCs suggests they may also contribute to the TeV $\gamma$-ray flux from evolved galaxies. We consider a scenario where this VHE emission from GCs is powered by electrons accelerated in communal stellar/pulsar wind cluster termination shocks. These electrons undergo inverse Compton scattering as they propagate into GC magnetotails. Our results show that the high-energy emission from GCs can be an important contributor to the GeV and TeV flux from massive, quiescent galaxies. The relative strength of each component depends on the global galactic properties and its evolutionary history.