  Context: The sub-Jovian or Neptunian desert is a previously-identified region
of parameter space where there is a relative dearth of intermediate-mass
planets at short orbital periods.
  Aims: We present the discovery of a new transiting planetary system within
the Neptunian desert, NGTS-14.
  Methods: Transits of NGTS-14Ab were discovered in photometry from the Next
Generation Transit Survey (NGTS). Follow-up transit photometry was conducted
from several ground-based facilities, as well as extracted from TESS full-frame
images. We combine radial velocities from the HARPS spectrograph with the
photometry in a global analysis to determine the system parameters.
  Results: NGTS-14Ab has a radius about 30 per cent larger than that of Neptune
($0.444\pm0.030~\mathrm{R_{Jup}}$), and is around 70 per cent more massive than
Neptune ($0.092 \pm 0.012~\mathrm{M_{Jup}}$). It transits the main-sequence K1
star, NGTS-14A, with a period of 3.54 days, just far enough to have maintained
at least some of its primordial atmosphere. We have also identified a possible
long-period stellar mass companion to the system, NGTS-14B, and we investigate
the binarity of exoplanet host stars inside and outside the Neptunian desert
using Gaia.
