We report the discovery of the first radio pulsar associated with NGC 6712, an eclipsing black widow (BW) pulsar, J1853$-$0842A, found by high-sensitivity searches using the Five-hundred-meter Aperture Spherical radio Telescope. This 2.15 ms pulsar is in a 3.56 hr compact circular orbit with a very low mass companion likely of mass 0.018 to 0.036 $M_{rm odot}$ and exhibits eclipsing of the pulsar signal. Though the distance to PSR J1853$-$0842A predicted from its dispersion measure ($155.125 pm 0.004$ cm$^{-3}$ pc) and Galactic free electron density models are about 30% smaller than that of NGC 6712 obtained from interstellar reddening measurements, this is likely due to limited knowledge about the spiral arms and Scutum stellar cloud in this direction. Follow-up timing observations spanning 445 days allow us to localize the pulsars position to be 0.14 core radii from the center of NGC 6712 and measure a negative spin-down rate for this pulsar of $-2.39(2)times10^{-21}rm s s^{-1}$. The latter cannot be explained without the acceleration of the GC and decisively supports the association between PSR J1853--0842A and NGC 6712. Considering the maximum GC acceleration, Galactic acceleration, and Shklovskii effect, we place an upper limit on the intrinsic spin-down rate to be $1.11times10^{-20}rm~s~s^{-1}$. From an analysis of the eclipsing observations, we estimate the electron density of the eclipse region to be about $1.88times10^6rm cm^{-3}$. We also place an upper limit of the accretion rate from the companion is about $3.05times10^{-13}~M_{rm odot}rm~yr^{-1}$ which is comparable with some other BWs.
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