Clustering tabular data remains a significant open challenge in data analysis and machine learning. Unlike for image data, similarity between tabular records often varies across datasets, making the definition of clusters highly dataset-dependent. Furthermore, the absence of supervised signals complicates hyperparameter tuning in deep learning clustering methods, frequently resulting in unstable performance. To address these issues and minimize the need for per-dataset tuning, we adopt an emerging approach in deep learning: zero-shot learning. We propose ZEUS, a self-contained model capable of clustering new datasets without any additional training or fine-tuning. It operates by decomposing complex datasets into meaningful components that can then be clustered effectively. Thanks to pre-training on synthetic datasets generated from a latent-variable prior, it generalizes across various datasets without requiring user intervention. To the best of our knowledge, ZEUS is the first zero-shot method capable of generating embeddings for tabular data in a fully unsupervised manner. Experimental results demonstrate that it performs on par with or better than traditional clustering algorithms and recent deep learning-based methods, while being significantly faster and more user-friendly.