We introduce Domain-Adaptive Prompt (DAP), a novel method for continual learning using Vision Transformers (ViT). Prompt-based continual learning has recently gained attention due to its rehearsal-free nature. Currently, the prompt pool, which is suggested by prompt-based continual learning, is key to effectively exploiting the frozen pre-trained ViT backbone in a sequence of tasks. However, we observe that the use of a prompt pool creates a domain scalability problem between pre-training and continual learning. This problem arises due to the inherent encoding of group-level instructions within the prompt pool. To address this problem, we propose DAP, a pool-free approach that generates a suitable prompt in an instance-level manner at inference time. We optimize an adaptive prompt generator that creates instance-specific fine-grained instructions required for each input, enabling enhanced model plasticity and reduced forgetting. Our experiments on seven datasets with varying degrees of domain similarity to ImageNet demonstrate the superiority of DAP over state-of-the-art prompt-based methods. Code is publicly available at https://github. com/naver-ai/dap-cl.