While vision-language models like CLIP have advanced zero-shot surgical phase recognition, they struggle with fine-grained surgical activities, especially action triplets. This limitation arises because current CLIP formulations rely on global image features, which overlook the fine-grained semantics and contextual details crucial for complex tasks like zero-shot triplet recognition. Furthermore, these models do not explore the hierarchical structure inherent in triplets, reducing their ability to generalize to novel triplets. To address these challenges, we propose fine-CLIP, which learns object-centric features and lever- ages the hierarchy in triplet formulation. Our approach integrates three components: hierarchical prompt modeling to capture shared semantics, LoRA-based vision backbone adaptation for enhanced feature extraction, and a graph-based condensation strategy that groups similar patch features into meaningful object clusters. Since triplet classification is a challenging task, we introduce an alternative yet meaningful base-to-novel generalization benchmark with two settings on the CholecT50 dataset: Unseen-Target, assessing adaptability to triplets with novel anatomical structures, and Unseen-Instrument-Verb, where models need to generalize to novel instrument-verb interactions. fine-CLIP shows significant improvements in F1 and mAP, enhancing zero-shot recognition of novel surgical triplets.