Integration of sectored antenna in wireless networks improves network performance through increased network capacity and extended transmission range. However, incorporating sectored antenna makes the trivial process of discovering neighbors even more challenging and complicated. Moreover, due to the duty-cycled nature of Wireless Sensor Networks (WSNs), self-adaptive and distributed neighbor discovery mechanisms are highly sought-after. In this paper, we present a Neighbor Discovery with Sectored Antenna (NDSA) protocol for WSNs with the sectored antenna. NDSA distinguish itself from other protocols in four distinct ways. Firstly, the introduction of super-frame like structure to support the duty-cycled operation of WSNs. Secondly, the protocol adapts its operation according to the network dynamics by leveraging the in-network information. Thirdly, a cooperative mechanism through which nodes utilize the information about their discovered neighbors to avoid an excessive exchange of control messages. Finally, handling the channel access details to discover neighbors faster with fewer message collisions. Through a comprehensive simulation-based study, the results show that the proposed protocol outperformed the random and serialized approaches to neighbor discovery in terms of discovery latency while significantly minimizing the communication overhead.