Large Language Models (LLMs) have demonstrated remarkable capabilities in machine translation. However, maintaining discourse coherence and terminological consistency remains a persistent challenge in document-level translation (DocMT). Existing solutions, such as memory-based agents, predominantly rely on explicit context concatenation. This paradigm treats historical context as a static external resource, which often leads to context dilution, high inference latency, and superficial knowledge integration. To address these limitations, we propose AdaDPI, an adaptive agentic framework that shifts the DocMT paradigm from static retrieval to dynamic parametric internalization. Specifically, we design a linguistic uncertainty monitor (LUM) to actively detect critical discourse discontinuities by the model’s epistemic uncertainty. Upon detection, a context-to-parameter integrator (CPI) compiles retrieved external constraints directly into the model’s intrinsic state via an online parameter adaptation mechanism. Through the online parameter adaptation on a lightweight adapter, AdaDPI internalizes document-specific norms into the model’s intrinsic representations, enabling a progressive evolution of the translation strategy as the discourse unfolds. Extensive experiments on the discourse-rich GuoFeng and IWSLT2017 datasets demonstrate that AdaDPI significantly outperforms the SoTA baselines by more than 5 points on the consistency metric.