Discovering new slots is critical to the success of dialogue systems. Most existing methods rely on automatic slot induction in unsupervised fashion or perform domain adaptation across zero or few-shot scenarios. They have difficulties in providing high-quality supervised signals to learn clustering-friendly features, and are limited in effectively transferring the prior knowledge from known slots to new slots. In this work, we propose a Semi-supervised Incremental Clustering method (SIC), to discover new slots with the aid of existing linguistic annotation models and limited known slot data. Specifically, we harvest slot value candidates with NLP model cues and innovatively formulate the slot discovery task under an incremental clustering framework. The model gradually calibrate slot representations under the supervision of generated pseudo-labels, and automatically learns to terminate when no more salient slot remains. Our thorough evaluation on five public datasets demonstrates that it significantly outperforms state-of-the-art models.