The rapid growth of climate science literature necessitates advanced information extraction (IE) systems to structure knowledge for researchers and policymakers. We introduce ClimateIE, a novel framework combining taxonomy-guided large language model (LLM) annotation with expert validation to address three core tasks: climate-specific named entity recognition, relationship extraction, and entity linking. Our contributions include: (1) the ClimateIE-Corpus—500 climate publications annotated via a hybrid human-AI pipeline with mappings to the extended GCMD+ taxonomy; (2) systematic evaluation showing Llama-3.3-70B achieves state-of-the-art performance (strict F1: 0.378 NER, 0.367 EL), outperforming larger commercial models (GPT-4o) and domain-adapted baselines (ClimateGPT) by 11-58%; and (3) analysis revealing critical challenges in technical relationship extraction (MountedOn: 0.000 F1) and emerging concept linking (26.4% unlinkable entities). Upon acceptance, we will release the corpus, toolkit, and guidelines to advance climate informatics, establishing benchmarks for NLP in Earth system science and underscoring the need for dynamic taxonomy governance and implicit relationship modeling.