Context-aware embedding methods boost retrieval accuracy by conditioning on corpus statistics (e.g., term co-occurrence and topical patterns) extracted from neighboring documents. However, this context-aware approach requires access to the target corpus or requires domain-specific finetuning, posing practical barriers in privacy-sensitive or resource-constrained settings. We present ZEST, a zero-shot contextual adaptation framework that replaces real corpus access with a one-time offline synthesis of a compact proxy. Given only a handful exemplar documents representative of the general target domain, we use a multi-step hierarchical procedure to generate a synthetic context corpus of several hundred documents that aims to emulate key domain-specific distributions. At inference, the frozen context-aware encoder uses this proxy corpus -- without any finetuning or target corpus access -- to produce domain-adapted embeddings. Across the MTEB benchmark, ZEST's zero-shot synthetic context adaptation using only five example documents performs within 0.5% of models leveraging full target corpus access -- demonstrating remarkable efficacy without any retraining. ZEST thus provides a practical method for deploying high-performance, adaptable embeddings in constrained environments.