Continual Generalized Category Discovery (C-GCD) requires identifying novel classes from unlabeled data while retaining knowledge of known classes over time. Existing methods typically update classifier weights dynamically, resulting in forgetting and inconsistent feature alignment. We propose GOAL, a unified framework that introduces a fixed Equiangular Tight Frame (ETF) classifier to impose a consistent geometric structure throughout learning. GOAL conducts supervised alignment for labeled samples and confidence-guided alignment for novel samples, enabling stable integration of new classes without disrupting old ones. Experiments on four benchmarks show that GOAL outperforms the prior method Happy, reducing forgetting by 16.1% and boosting novel class discovery by 3.2%, establishing a strong solution for long-horizon continual discovery.