We propose an enhanced access reservation protocol (ARP) with a partial preamble transmission mechanism for the narrow band Internet of Things (NB-IoT) systems. The proposed ARP can enhance the ARP performance by mitigating the occurrence of preamble collisions, while being compatible with the conventional NB-IoT ARP. We provide an analytical model that captures the performance of the proposed ARP in terms of false alarm, misdetection, and collision probabilities. Moreover, we investigate a tradeoff between the misdetection and the collision probabilities, and optimize the proposed ARP according to the system loads. The results show that the proposed ARP outperforms the conventional NB-IoT ARP, in particular, at heavier system loads.