Analyzing Spitzer and Herschel archival measurements we identified a hitherto unknown debris disk around the young K7/M0 star CP-72 2713. The system belongs to the 24Myr old $\beta$ Pic moving group. Our new 1.33mm continuum observation, obtained with the ALMA 7-m array, revealed an extended dust disk with a peak radius of 140au, probably tracing the location of the planetesimal belt in the system. The disk is outstandingly large compared to known spatially resolved debris disks and also to protoplanetary disks around stars of comparable masses. The dynamical excitation of the belt at this radius is found to be reconcilable with planetary stirring, while self-stirring by large planetesimals embedded in the belt can work only if these bodies form very rapidly, e.g. via pebble concentration. By analyzing the spectral energy distribution we derived a characteristic dust temperature of 43K and a fractional luminosity of 1.1$\times$10$^{-3}$. The latter value is prominently high, we know only four other similarly dust-rich Kuiper-belt analogs within 40pc of the Sun.