Fully supervised continual learning methods have shown improved attack traffic detection in a closed-world learning setting. However, obtaining fully annotated data is an arduous task in the security domain. Further, our research finds that after training a classifier on two days of network traffic, the performance decay of attack class detection over time (computed using the area under the time on precision-recall AUC of the attack class) drops from 0.985 to 0.506 on testing with three days of new test samples. In this work, we focus on label scarcity and open-world learning (OWL) settings to improve the attack class detection of the continual learning-based network intrusion detection (NID). We formulate OWL for NID as a semi-supervised continual learning-based method, dubbed SOUL, to achieve the classifier performance on par with fully supervised models while using limited annotated data. The proposed method is motivated by our empirical observation that using gradient projection memory (constructed using buffer memory samples) can significantly improve the detection performance of the attack (minority) class when trained using partially labeled data. Further, using the classifier's confidence in conjunction with buffer memory, SOUL generates high-confidence labels whenever it encounters OWL tasks closer to seen tasks, thus acting as a label generator. Interestingly, SOUL efficiently utilizes samples in the buffer memory for sample replay to avoid catastrophic forgetting, construct the projection memory, and assist in generating labels for unseen tasks. The proposed method is evaluated on four standard network intrusion detection datasets, and the performance results are closer to the fully supervised baselines using at most 20% labeled data while reducing the data annotation effort in the range of 11 to 45% for unseen data.