We report the discovery of the transiting exoplanet NGTS-12b by the Next Generation Transit Survey (NGTS). The host star, NGTS-12, is a V=12.38 mag star with an effective temperature of T=$5690\pm 130$ K. NGTS-12b orbits with a period of $P=7.53$d, making it the longest period planet discovered to date by the main NGTS survey. We verify the NGTS transit signal with data extracted from the TESS full-frame images, and combining the photometry with radial velocity measurements from HARPS and FEROS we determine NGTS-12b to have a mass of $0.208\pm 0.022$ M and a radius of $1.048\pm 0.032$ R. NGTS-12b sits on the edge of the Neptunian desert when we take the stellar properties into account, highlighting the importance of considering both the planet and star when studying the desert. The long period of NGTS-12b combined with its low density of just $0.223\pm 0.029$ g cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$ make it an attractive target for atmospheric characterization through transmission spectroscopy with a Transmission Spectroscopy Metric of 89.4.