Idiom translation remains a formidable challenge for Large Language Models (LLMs), as the constraints of static parametric memory and the noise in sentence-level retrieval often lead to literal misinterpretations. To address this, we propose DeReA, a detect-retrieve-arbitrate framework. The system employs a preference-aligned detector to identify idiomatic spans by reasoning over semantic conflicts between literal and contextual meanings. Subsequently, an idiom-centric translator invokes a fine-tuned embedding model to efficiently retrieve canonical definitions from an external knowledge base. The translator then utilizes a dual-path arbitration mechanism to select the optimal rendering by weighing the retrieval-augmented translations against direct translation. To evaluate our framework, we introduce LoMI, a high-difficulty benchmark with low data contamination. Experimental results demonstrate that DeReA significantly enhances performance across various model scales, improving GPT-5-mini by over 5.2 points in both idiomatic quality and consistency according to LLM-based metrics. Furthermore, evaluations on an emerging slang dataset from Urban Dictionary validate the potential of our approach in handling novel and evolving linguistic data. Our code is available at https://github.com/jrongqing/DeReA.