Selecting check-worthy claims for fact-checking is considered a crucial part of expediting the fact-checking process by filtering out and ranking the check-worthy claims for being validated among the impressive amount of claims could be found online. The check-worthy claim detection task, however, becomes more challenging when the model needs to deal with new topics that differ from those seen earlier. In this study, we propose a domain-adaptation framework for check-worthy claims detection across topics for the Arabic language to adopt a new topic, mimicking a real-life scenario of the daily emergence of events worldwide. We propose the Gradual Topic Learning (GTL) model, which builds an ability to learning gradually and emphasizes the check-worthy claims for the target topic during several stages of the learning process. In addition, we introduce the Similarity-driven Gradual Topic Learning (SGTL) model that synthesizes gradual learning with a similarity-based strategy for the target topic. Our experiments demonstrate the effectiveness of our proposed model, showing an overall tendency for improving performance over the state-of-the-art baseline across 11 out of the 14 topics under study.