WiFi-based human activity recognition (HAR) holds significant application potential across various fields. To handle dynamic environments where new activities are continuously introduced, WiFi-based HAR systems must adapt by learning new concepts without forgetting previously learned ones. Furthermore, retaining knowledge from old activities by storing historical exemplar is impractical for WiFi-based HAR due to privacy concerns and limited storage capacity of edge devices. In this work, we propose ConSense, a lightweight and fast-adapted exemplar-free class incremental learning framework for WiFi-based HAR. The framework leverages the transformer architecture and involves dynamic model expansion and selective retraining to preserve previously learned knowledge while integrating new information. Specifically, during incremental sessions, small-scale trainable parameters that are trained specifically on the data of each task are added in the multi-head self-attention layer. In addition, a selective retraining strategy that dynamically adjusts the weights in multilayer perceptron based on the performance stability of neurons across tasks is used. Rather than training the entire model, the proposed strategies of dynamic model expansion and selective retraining reduce the overall computational load while balancing stability on previous tasks and plasticity on new tasks. Evaluation results on three public WiFi datasets demonstrate that ConSense not only outperforms several competitive approaches but also requires fewer parameters, highlighting its practical utility in class-incremental scenarios for HAR.