  Recent observations have shown that pulsars are surrounded by extended
regions which emit TeV-scale gamma rays through the inverse Compton scattering
of very high energy electrons and positrons. Such TeV halos are responsible for
a large fraction of the Milky Way's TeV-scale gamma-ray emission. In this
paper, we calculate the gamma-ray spectrum from the population of TeV halos
located within the Andromeda Galaxy, predicting a signal that is expected to be
detectable by the Cherenkov Telescope Array (CTA). We also calculate the
contribution from TeV halos to the isotropic gamma-ray background (IGRB),
finding that these sources should contribute significantly to this flux at the
highest measured energies, constituting up to $\sim 20\%$ of the signal
observed above $\sim 0.1 \, {\rm TeV}$.
