The curing system plays a vital role in designing rubber compounds for various industrial applications. Therefore, it is paramount to establish viable curing strategies for any new elastomer to explore its application potentials and commercial significance. Impacts of different curing regimes on the properties of a recently developed copolymer of chloroprene and acrylonitrile (acrylonitrile-chloroprene rubber, NCR) are reported here. Several primary accelerators (four from thiourea- and one from thiazolene product families) were used for curing the new rubber along with fixed loadings of zinc oxide (5 phr) and magnesium oxide (4 phr). Besides, curatives based on sulfur and peroxide were also evaluated. The influence of different curing systems on the rheological and physical properties of the copolymer was explored. It has been seen that the properties of the copolymer are considerably influenced by the different curing systems used. While ethylene thiourea (ETU) and propylene thiourea (PTU), as primary accelerators, provide the highest state of cure but may cause scorch. The use of trimethyl thiourea (TMU), on the other hand, results in the fastest rate and the most stable state of cure, good scorch safety, bin stability, and an overall good balance of properties. The sulfur-based crosslinking system induces good mechanical properties but causes limited bin stability, poor high-temperature compression set, and impaired heat resistance properties. As a curing agent, peroxide delivers the best bin stability in the rubber stocks but yields higher stiffness and limited aging resistance in the vulcanizates.