Adopting contrastive image-text pretrained models like CLIP towards video classification has gained attention due to its cost-effectiveness and competitive performance. However, recent works in this area face a trade-off. Fine-tuning the pretrained model to achieve strong supervised performance results in low zero-shot generalization. Similarly, freezing the backbone to retain zero-shot capability causes significant drop in supervised accuracy. Because of this, recent works in literature typically train separate models for supervised and zero-shot action recognition. In this work, we propose a multimodal prompt learning scheme that works to balance the supervised and zero-shot performance under a single unified training. Our prompting approach on the vision side caters for three aspects: 1) Global video-level prompts to model the data distribution; 2) Local frame-level prompts to provide per-frame discriminative conditioning; and 3) a summary prompt to extract a condensed video representation. Additionally, we define a prompting scheme on the text side to augment the textual context. Through this prompting scheme, we can achieve state-of-the-art zero-shot performance on Kinetics-600, HMDB51 and UCF101 while remaining competitive in the supervised setting. By keeping the pretrained backbone frozen, we optimize a much lower number of parameters and retain the existing general representation which helps achieve the strong zero-shot performance. Our codes/models will be released at https://github.com/TalalWasim/Vita-CLIP..