Abstract The Green Bank North Celestial Cap survey is a 350 MHz all-sky survey for pulsars and fast radio transients using the Robert C. Byrd Green Bank Telescope. To date, the survey has discovered over 190 pulsars, including 33 millisecond pulsars and 24 rotating radio transients. Several exotic pulsars have been discovered in the survey, including PSR J1759+5036, a binary pulsar with a 176 ms spin period in an orbit with a period of 2.04 days, an eccentricity of 0.3, and a projected semi-major axis of 6.8 light seconds. Using seven years of timing data, we are able to measure one post–Keplerian parameter, advance of periastron, which has allowed us to constrain the total system mass to 2.62 ± 0.03 M _⊙. This constraint, along with the spin period and orbital parameters, suggests that this is a double neutron star system, although we cannot entirely rule out a pulsar-white dwarf binary. This pulsar is only detectable in roughly 45% of observations, most likely due to scintillation. However, additional observations are required to determine whether there may be other contributing effects.