Understanding the semantics of relational tables is instrumental for automation in data exploration and preparation systems. A key source for understanding a table is the semantics of its columns. With the rise of deep learning, learned table representations are now available, which can be applied for semantic type detection and achieve good performance on benchmarks. Nevertheless, we observe a gap between this performance and its applicability in practice. In this paper, we propose AdaTyper to address one of the most critical deployment challenges: adaptation. AdaTyper uses weak-supervision to adapt a hybrid type predictor towards new semantic types and shifted data distributions at inference time, using minimal human feedback. The hybrid type predictor of AdaTyper combines rule-based methods and a light machine learning model for semantic column type detection. We evaluate the adaptation performance of AdaTyper on real-world database tables hand-annotated with semantic column types through crowdsourcing and find that the f1-score improves for new and existing types. AdaTyper approaches an average precision of 0.6 after only seeing 5 examples, significantly outperforming existing adaptation methods based on human-provided regular expressions or dictionaries.