We present the gradual style adaptor TTS (GSA-TTS) with a novel style encoder that gradually encodes speaking styles from an acoustic reference for zero-shot speech synthesis. GSA first captures the local style of each semantic sound unit. Then the local styles are combined by self-attention to obtain a global style condition. This semantic and hierarchical encoding strategy provides a robust and rich style representation for an acoustic model. We test GSA-TTS on unseen speakers and obtain promising results regarding naturalness, speaker similarity, and intelligibility. Additionally, we explore the potential of GSA in terms of interpretability and controllability, which stems from its hierarchical structure.