Open-domain Knowledge Graph Completion (KGC) faces significant challenges in an ever-changing world, especially when considering the continual emergence of new entities in daily news. Existing approaches for KGC mainly rely on pretrained language models' parametric knowledge, pre-constructed queries, or single-step retrieval, typically requiring substantial supervision and training data. Even so, they often fail to capture comprehensive and up-to-date information about unpopular and/or emerging entities. To this end, we introduce Agentic Reasoning for Emerging Entities (AgREE), a novel agent-based framework that combines iterative retrieval actions and multi-step reasoning to dynamically construct rich knowledge graph triplets. Experiments show that, despite requiring zero training efforts, AgREE significantly outperforms existing methods in constructing knowledge graph triplets, especially for emerging entities that were not seen during language models' training processes, outperforming previous methods by up to 13.7%. Moreover, we propose a new evaluation methodology that addresses a fundamental weakness of existing setups and a new benchmark for KGC on emerging entities. Our work demonstrates the effectiveness of combining agent-based reasoning with strategic information retrieval for maintaining up-to-date knowledge graphs in dynamic information environments.