Spatial Transcriptomics (ST) merges the benefits of pathology images and gene expression, linking molecular profiles with tissue structure to analyze spot-level function comprehensively. Predicting gene expression from histology images is a cost-effective alternative to expensive ST technologies. However, existing methods mainly focus on spot-level image-to-gene matching but fail to leverage the full hierarchical structure of ST data, especially on the gene expression side, leading to incomplete image-gene alignment. Moreover, a challenge arises from the inherent information asymmetry: gene expression profiles contain more molecular details that may lack salient visual correlates in histological images, demanding a sophisticated representation learning approach to bridge this modality gap. We propose HyperST, a framework for ST prediction that learns multi-level image-gene representations by modeling the data's inherent hierarchy within hyperbolic space, a natural geometric setting for such structures. First, we design a Multi-Level Representation Extractors to capture both spot-level and niche-level representations from each modality, providing context-aware information beyond individual spot-level image-gene pairs. Second, a Hierarchical Hyperbolic Alignment module is introduced to unify these representations, performing spatial alignment while hierarchically structuring image and gene embeddings. This alignment strategy enriches the image representations with molecular semantics, significantly improving cross-modal prediction. HyperST achieves state-of-the-art performance on four public datasets from different tissues, paving the way for more scalable and accurate spatial transcriptomics prediction.