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The MMGPS-L is the most sensitive pulsar survey in the Southern Hemisphere.We present a follow-up study of one of these new discoveries, PSR J1208-5936, a28.71-ms recycled pulsar in a double neutron star system with an orbital periodof Pb=0.632 days and an eccentricity of e=0.348. Through timing of almost oneyear of observations, we detected the relativistic advance of periastron(0.918(1) deg/yr), resulting in a total system mass of Mt=2.586(5) Mo. We alsoachieved low-significance constraints on the amplitude of the Einstein delayand Shapiro delay, in turn yielding constraints on the pulsar mass(Mp=1.26(+0.13/-0.25) Mo), the companion mass (Mc=1.32(+0.25/-0.13) Mo, and theinclination angle (i=57(12) degrees). This system is highly eccentric comparedto other Galactic field double neutron stars with similar periods, possiblyhinting at a larger-than-usual supernova kick during the formation of thesecond-born neutron star. The binary will merge within 7.2(2) Gyr due to theemission of gravitational waves. With the improved sensitivity of the MMGPS-L,we updated the Milky Way neutron star merger rate to be 25(+19/-9) Myr$^{-1}$within 90% credible intervals, which is lower than previous studies based onknown Galactic binaries owing to the lack of further detections despite thehighly sensitive nature of the survey. This implies a local cosmic neutron starmerger rate of 293(+222/-103} Gpc/yr, consistent with LIGO and Virgo O3observations. With this, we predict the observation of 10(+8/-4) neutron starmerger events during the LIGO-Virgo-KAGRA O4 run. We predict the uncertaintieson the component masses and the inclination angle will be reduced to5x10$^{-3}$ Mo and 0.4 degrees after two decades of timing, and that in atleast a decade from now the detection of the shift in Pb and the sky propermotion will serve to make an independent constraint of the distance to thesystem.

The MPIfR-MeerKAT Galactic Plane Survey II. The eccentric double neutron star system PSR J1208-5936 and a neutron star merger rate update