We present the discovery and timing of the young (age $sim 28.6$ kyr) pulsar PSR J0837$-$2454. Based on its high latitude ($b = 9.8^{circ}$) and dispersion measure (DM $ = 143$~pc~cm$^{-3}$), the pulsar appears to be at a $z$-height of $>$1 kpc above the Galactic plane, but near the edge of our Galaxy. This is many times the observed scale height of the canonical pulsar population, which suggests this pulsar may have been born far out of the plane. If accurate, the young age and high $z$-height imply that this is the first pulsar known to be born from a runaway O/B star. In follow-up imaging with the Australia Telescope Compact Array (ATCA), we detect the pulsar with a flux density $S_{1400} = 0.18 pm 0.05$ mJy. We do not detect an obvious supernova remnant around the pulsar in our ATCA data, but we detect a co-located, low-surface-brightness region of $sim$1.5$^circ$ extent in archival Galactic and Extragalactic All-sky MWA Survey data. We also detect co-located H$alpha$ emission from the Southern H$alpha$ Sky Survey Atlas. Distance estimates based on these two detections come out to $sim$0.9 kpc and $sim$0.2 kpc respectively, both of which are much smaller than the distance predicted by the NE2001 model ($6.3$ kpc) and YMW model ($>25$ kpc) and place the pulsar much closer to the plane of the Galaxy. If the pulsar/remnant association holds, this result also highlights the inherent difficulty in the classification of transients as Galactic (pulsar) or extragalactic (fast radio burst) toward the Galactic anti-center based solely on the modeled Galactic electron contribution to a detection.
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