  We present the discovery of NGTS J214358.5-380102, an eccentric M-dwarf
binary discovered by the Next Generation Transit Survey. The system period of
7.618 days is greater than many known eclipsing M-dwarf binary systems. Its
orbital eccentricity of $0.323^{+0.0014}_{-0.0037}$, is large relative to the
period and semi-major axis of the binary. Global modelling of photometry and
radial velocities indicate stellar masses of $M_A$=$0.426
^{+0.0056}_{-0.0049}$, $M_B$=$0.455 ^{+0.0058}_{-0.0052}$ and stellar radii
$R_A$=$0.461 ^{+0.038}_{-0.025}$ $R_B$=$0.411 ^{+0.027}_{-0.039}$,
respectively. Comparisons with stellar models for low mass stars show that one
star is consistent with model predictions whereas the other is substantially
oversized. Spectral analysis of the system suggests a primary of spectral type
M3V, consistent with both modelled masses and radii, and with SED fitting of
NGTS photometry. As the most eccentric eclipsing M-dwarf binary known, NGTS
J214358.5-380102 provides an interesting insight into the strength of tidal
effects in the circularisation of stellar orbits.
