We report the discovery of a bow-shock pulsar wind nebula (PWN), named Potoroo, and the detection of a young pulsar J1638$-$4713 that powers the nebula. We present a radio continuum study of the PWN based on 20-cm observations obtained from the Australian Square Kilometre Array Pathfinder (ASKAP) and MeerKAT. PSR J1638$-$4713 was identified using Parkes radio telescope observations at frequencies above 3 GHz. The pulsar has the second-highest dispersion measure of all known radio pulsars (1 553 pc cm$^{-3}$), a spin period of 65.74 ms and a spin-down luminosity of $\dot{E}=6.1\times10^{36}$ erg s$^{-1}$. The PWN has a cometary morphology and one of the greatest projected lengths among all the observed pulsar radio tails, measuring over 21 pc for an assumed distance of 10 kpc. The remarkably long tail and atypically steep radio spectral index are attributed to the interplay of a supernova reverse shock and the PWN. The originating supernova remnant is not known so far. We estimated the pulsar kick velocity to be in the range of 1 000–2 000 km s$^{-1}$ for ages between 23 and 10 kyr. The X-ray counterpart found in Chandra data, CXOU J163802.6$-$471358, shows the same tail morphology as the radio source but is shorter by a factor of 10. The peak of the X-ray emission is offset from the peak of the radio total intensity (Stokes $\rm I$) emission by approximately 4.7$^{\prime\prime}$, but coincides well with circularly polarised (Stokes $\rm V$) emission. No infrared counterpart was found.