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(abridged) In this work we present the results of one year of upgraded GiantMetrewave Radio Telescope timing measurements of PSR~J0514$-$4002A, a 4.99-mspulsar in a 18.8-day, eccentric ($e \, =\, 0.89$) orbit with a massivecompanion located in the globular cluster NGC~1851. Combining these data withearlier Green Bank Telescope data, we greatly improve the precision of the rateof advance of periastron, $\dot{\omega} \, = \, 0.0129592(16)\, \deg \, \rmyr^{-1}$ which, assuming the validity of general relativity, results in a muchrefined measurement of the total mass of the binary, $M_{\rm tot} \, = \,2.4730(6) \, M_{\odot}$. Additionally, we measure the Einstein delay parameter,$\gamma\,, = \, 0.0216(9) \, \rm s$. Furthermore, we measure the proper motionof the system ($\mu_{\alpha} \, = \, 5.19(22)$ and $\mu_{\delta} =-0.56(25)\rm~mas ~ yr^{-1}$), which is not only important for analyzing itsmotion in the cluster, but is also essential for a proper interpretation of$\gamma$, given the latter parameter's correlation with the variation of theprojected semi-major axis. The measurements of $\gamma$ and the proper motionenable a separation of the system component masses: we obtain a pulsar mass of$M_{p} \, = \, 1.25^{+0.05}_{-0.06} \, M_{\odot}$ and a companion mass of$M_{c} \, = \, 1.22^{+0.06}_{-0.05} \, M_{\odot}$. This raises the possibilitythat the companion is also a neutron star. Searches for radio pulsations fromthe companion have thus far been unsuccessful, hence we cannot confirm thelatter hypothesis. The low mass of this millisecond pulsar - one of the lowestever measured for such objects - clearly indicates that the recycling processcan be achieved with a relatively small amount of mass transfer.

Upgraded Giant Metrewave Radio Telescope timing of NGC 1851A: a possible millisecond pulsar-neutron star system