This paper investigates the problem of distributed online learning of generalized Nash equilibrium (GNE) in an online multi-cluster game, where each agent is associated with time-varying local cost functions and is subject to time-varying coupling constraints. At each time step, each agent only observes the values of its local cost and constraint functions after decision-making, without access to their full information. The goal of each agent within a cluster is to collaboratively optimize the cluster’s cost function over time while satisfying the time-varying coupled inequality constraints and local constraint sets, despite the absence of gradient information. To tackle this challenge, a zeroth-order distributed online GNE learning algorithm is proposed, which leverages an unbiased gradient estimator to enable agents to learn the time-varying GNE. Theoretical analysis demonstrates that the proposed algorithm achieves sublinear expected dynamic regret and constraint violation, provided that the path variation of the GNE sequence grows sublinearly. Finally, simulation results on a distributed tracking problem validate the effectiveness of the proposed algorithm.