Entity recognition in Automatic Speech Recognition (ASR) is challenging for rare and domain-specific terms. In domains such as finance, medicine, and air-traffic control, these errors are costly. If an entity is entirely absent from the ASR output, text-only post-correction has little signal to recover it. To address this, we introduce RECOVER, an agentic post-ASR entity-correction framework. It leverages multiple hypotheses as evidence from ASR, retrieves relevant entities, proposes Large Language Model (LLM) correction under constraints, filters them through deterministic guardrails and uses an LLM critic that judges each surviving edit and can trigger a targeted feedback round to recover an entity the first pass missed. The hypotheses are used by one of several strategies, namely 1-Best, Entity-Aware Select, Recognizer Output Voting Error Reduction (ROVER) Ensemble, LLM-Select and Adaptive Routing. Evaluated across five diverse datasets over a Whisper-large-v3 baseline, it achieves up to 49% relative reduction in entity-phrase word error rate (E-WER) and increases entity recall by up to 14 percentage points while preserving the overall word error rate (WER), with LLM-Select the strongest strategy.