Exozodis are analogs to the Solar System Zodiacal cloud, a collection of dust grains orbiting inner to the Asteroid Belt and down to the dust sublimation radius. Exozodiacal dust is short-lived, relative to the age of the exoplanetary systems in which it is observed, and impossible to produce in-situ via collisions among parent bodies. It implies an external replenishment mechanism from a distant reservoir, such as the evaporation of comets detached from parent belts analogous to the Kuiper and Asteroid belts. As these parent belts themselves are not replenished over time, the trend for more frequent exozodi detection in old (>100 Myr) than young systems is thus surprising. A recent study has shown that planetesimals in inner mean motion resonance (MMR) with a planet of low eccentricity can be scattered onto comet-like orbits, and sustain exozodi replenishment at observed levels over Gyr timescales. Here we extend this study to the case of outer MMR, combining analytical predictions and numerical simulations. We show that continuous production of active comets over Gyr timescales producing dust levels comparable to detected exozodis can also be sustained and from reservoirs as mature and little massive as the Kuiper Belt.