The progress in hyperbolic neural networks (HNNs) research is hindered by their absence of inductive bias mechanisms, which are essential for generalizing to new tasks and facilitating scalable learning over large datasets. In this paper, we aim to alleviate these issues by learning generalizable inductive biases from the nodes’ local subgraph and transfer them for faster learning over new subgraphs with a disjoint set of nodes, edges, and labels in a few-shot setting. We introduce a novel method, Hyperbolic GRAph Meta Learner (H-GRAM), that, for the tasks of node classification and link prediction, learns transferable information from a set of support local subgraphs in the form of hyperbolic meta gradients and label hyperbolic protonets to enable faster learning over a query set of new tasks dealing with disjoint subgraphs. Furthermore, we show that an extension of our meta-learning framework also mitigates the scalability challenges seen in HNNs faced by existing approaches. Our comparative analysis shows that H-GRAM effectively learns and transfers information in multiple challenging few-shot settings compared to other state-of-the-art baselines. Additionally, we demonstrate that, unlike standard HNNs, our approach is able to scale over large graph datasets and improve performance over its Euclidean counterparts.