Entity Linking (EL) has traditionally relied on large annotated datasets and extensive model fine-tuning. While recent few-shot methods leverage large language models (LLMs) through prompting to reduce training requirements, they often suffer from inefficiencies due to expensive LLM-based reasoning. ARTER (Adaptive Routing and Targeted Entity Reasoning) presents a structured pipeline that achieves high performance without deep fine-tuning by strategically combining candidate generation, context-based scoring, adaptive routing, and selective reasoning. ARTER computes a small set of complementary signals (both embedding and LLM-based) over the retrieved candidates to categorize contextual mentions into easy and hard cases. The cases are then handled by low-computational entity linker (e.g. ReFinED) and more expensive targeted LLM-based reasoning respectively. On standard benchmarks, ARTER outperforms ReFinED by up to +4.13\%, with an average gain of +2.47\% on 5 out of 6 datasets, and performs comparably to pipelines using LLM-based reasoning for all mentions, while being twice efficient in terms of the number of LLM tokens.