Test Time Adaptation (TTA) is a pivotal concept in machine learning, enabling models to perform well in real-world scenarios, where test data distribution differs from training. In this work, we propose a novel approach called pseudo Source guided Target Clustering (pSTarC) addressing the relatively unexplored area of TTA under real-world domain shifts. This method draws inspiration from target clustering techniques and exploits the source classifier for generating pseudo-source samples. The test samples are strategically aligned with these pseudo-source samples, facilitating their clustering and thereby enhancing TTA performance. pSTarC operates solely within the fully test-time adaptation protocol, removing the need for actual source data. Experimental validation on a variety of domain shift datasets, namely VisDA, Office-Home, DomainNet-126, CIFAR-100C verifies pSTarC's effectiveness. This method exhibits significant improvements in prediction accuracy along with efficient computational requirements. Furthermore, we also demonstrate the universality of the pSTarC framework by showing its effectiveness for the continuous TTA framework. The source code for our method is available at https://manogna-s.github.io/pstarc