Existing algorithms for human body part segmentation have shown promising results on challenging datasets, primarily relying on end-to-end supervision. However, these algorithms exhibit severe performance drops in the face of domain shifts, leading to inaccurate segmentation masks. To tackle this issue, we introduce POSTURE: \underline{Po}se Guided Un\underline{s}upervised Domain Adap\underline{t}ation for H\underline{u}man Body Pa\underline{r}t S\underline{e}gmentation - an innovative pseudo-labelling approach designed to improve segmentation performance on the unlabeled target data. Distinct from conventional domain adaptive methods for general semantic segmentation, POSTURE stands out by considering the underlying structure of the human body and uses anatomical guidance from pose keypoints to drive the adaptation process. This strong inductive prior translates to impressive performance improvements, averaging 8\% over existing state-of-the-art domain adaptive semantic segmentation methods across three benchmark datasets. Furthermore, the inherent flexibility of our proposed approach facilitates seamless extension to source-free settings (SF-POSTURE), effectively mitigating potential privacy and computational concerns, with negligible drop in performance.