We report the discovery of a Neptune-like planet (LP 714-47 b, P = 4.05204 d, m_b = 30.8 ± 1.5M_⊕, R_b = 4.7 ± 0.3 R_⊕) located in the “hot Neptune desert”. Confirmation of the TESS Object of Interest (TOI 442.01) was achieved with radial-velocity follow-up using CARMENES, ESPRESSO, HIRES, iSHELL, and PFS, as well as from photometric data using TESS, Spitzer, and ground-based photometry from MuSCAT2, TRAPPIST-South, MONET-South, the George Mason University telescope, the Las Cumbres Observatory Global Telescope network, the El Sauce telescope, the TÜBİTAK National Observatory, the University of Louisville Manner Telescope, and WASP-South. We also present high-spatial resolution adaptive optics imaging with the Gemini Near-Infrared Imager. The low uncertainties in the mass and radius determination place LP 714-47 b among physically well-characterised planets, allowing for a meaningful comparison with planet structure models. The host star LP 714-47 is a slowly rotating early M dwarf (T_eff = 3950 ± 51 K) with a mass of 0.59 ± 0.02M_⊙ and a radius of 0.58 ± 0.02R_⊙. From long-term photometric monitoring and spectroscopic activity indicators, we determine a stellar rotation period of about 33 d. The stellar activity is also manifested as correlated noise in the radial-velocity data. In the power spectrum of the radial-velocity data, we detect a second signal with a period of 16 days in addition to the four-day signal of the planet. This could be shown to be a harmonic of the stellar rotation period or the signal of a second planet. It may be possible to tell the difference once more TESS data and radial-velocity data are obtained.