ABSTRACT Very little is known about the young planet population because the detection of small planets orbiting young stars is obscured by the effects of stellar activity and fast rotation, which mask planets within radial velocity and transit data sets. The few planets that have been discovered in young clusters generally orbit stars too faint for any detailed follow-up analysis. Here, we present the characterization of a new mini-Neptune planet orbiting the bright (V = 9) and nearby K2 dwarf star, HD 18599. The planet candidate was originally detected in TESS light curves from sectors 2, 3, 29, and 30, with an orbital period of 4.138 d. We then used HARPS and FEROS radial velocities, to find the companion mass to be 25.5$\pm$4.6 $M_{\oplus }$. When we combine this with the measured radius from TESS of 2.70$\pm$0.05 $R_{\oplus }$, we find a high planetary density of 7.1$\pm$1.4 g cm$^{-3}$. The planet exists on the edge of the Neptune Desert and is the first young planet (300 Myr) of its type to inhabit this region. Structure models argue for a bulk composition to consist of 23 per cent H$_2$O and 77 per cent Rock and Iron. Future follow-up with large ground- and space-based telescopes can enable us to begin to understand in detail the characteristics of young Neptunes in the galaxy.