We propose Adapter Merging with Centroid Prototype Mapping (ACMap), an exemplar-free framework for class-incremental learning (CIL) that addresses both catastrophic forgetting and scalability. While existing methods trade-off between inference time and accuracy, ACMap consolidates task-specific adapters into a single adapter, ensuring constant inference time across tasks without compromising accuracy.The framework employs adapter merging to build a shared subspace that aligns task representations and mitigates forgetting, while centroid prototype mapping maintains high accuracy through consistent adaptation in the shared subspace. To further improve scalability, an early stopping strategy limits adapter merging as tasks increase. Extensive experiments on five benchmark datasets demonstrate that ACMap matches state-of-the-art accuracy while maintaining inference speed comparable to the fastest existing methods.