  We report the discovery of the first new pulsar with the Murchison Widefield
Array (MWA), PSR J0036$-$1033, a long-period (0.9 s) nonrecycled pulsar with a
dispersion measure (DM) of 23.1 ${\rm pc\,cm^{-3}}$. It was found after
processing only a small fraction ($\sim$1%) of data from an ongoing all-sky
pulsar survey. Follow-up observations have been made with the MWA, the upgraded
Giant Metrewave Radio Telescope (uGMRT), and the Parkes 64 m telescopes,
spanning a frequency range from $\sim$150 MHz to 4 GHz. The pulsar is faint,
with an estimated flux density ($S$) of $\sim$1 mJy at 400 MHz and a spectrum
$S(\nu)\,\propto\,\nu^{-2.0 \pm 0.2}$, where $\nu$ is frequency. The DM-derived
distance implies that it is also a low-luminosity source ($\sim$ 0.1 ${\rm
mJy\,kpc^2}$ at 1400 MHz). The analysis of archival MWA observations reveals
that the pulsar's mean flux density varies by up to a factor of $\sim$5-6 on
timescales of several weeks to months. By combining MWA and uGMRT data, the
pulsar position was determined to arcsecond precision. We also report on
polarization properties detected in the MWA and Parkes bands. The pulsar's
nondetection in previous pulsar and continuum imaging surveys, the observed
high variability, and its detection in a small fraction of the survey data
searched to date, all hint at a larger population of pulsars that await
discovery in the southern hemisphere, with the MWA and the future low-frequency
Square Kilometre Array.
