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The rapidly changing landscape of technology and industries leads to dynamic skill requirements, making it crucial for employees and employers to anticipate such shifts to maintain a competitive edge in the labor market. Existing efforts in this area either relies on domain-expert knowledge or regarding the skill evolution as a simplified time series forecasting problem. However, both approaches overlook the sophisticated relationships among different skills and the inner-connection between skill demand and supply variations. In this paper, we propose a Cross-view Hierarchical Graph learning Hypernetwork (CHGH) framework for joint skill demand-supply prediction. Specifically, CHGH is an encoder-decoder network consisting of i) a cross-view graph encoder to capture the interconnection between skill demand and supply, ii) a hierarchical graph encoder to model the co-evolution of skills from a cluster-wise perspective, and iii) a conditional hyper-decoder to jointly predict demand and supply variations by incorporating historical demand-supply gaps. Extensive experiments on three real-world datasets demonstrate the superiority of the proposed framework compared to seven baselines and the effectiveness of the three modules.