While Knowledge Graph Completion (KGC) on static facts is a matured field, Temporal Knowledge Graph Completion (TKGC), that incorporates validity time into static facts is still in its nascent stage. The KGC methods fall into multiple categories including embedding-based, rule-based, GNN-based, pretrained Language Model based approaches. However, such dimensions have not been explored in TKG. To that end, we propose a novel temporal neuro-symbolic model, NeuSTIP, that performs link prediction and time interval prediction in a TKG. NeuSTIP learns temporal rules in the presence of the Allen predicates that ensure the temporal consistency between neighboring predicates in a given rule. We further design a unique scoring function that evaluates the confidence of the candidate answers while performing link prediction and time interval prediction by utilizing the learned rules. Our empirical evaluation on two time interval based TKGC datasets suggests that our model outperforms state-of-the-art models for both link prediction and the time interval prediction task.