Multi-hop Knowledge Graph Question Answering (KGQA) requires coherent reasoning across relational paths, yet existing methods often treat each reasoning step independently and fail to effectively leverage experience from prior explorations, leading to fragmented reasoning and redundant exploration. To address these challenges, we propose Trajectoryaware Reasoning with Adaptive Context and Exploration priors (TRACE), an experiential framework that unifies LLM-driven contextual reasoning with exploration prior integration to enhance the coherence and robustness of multihop KGQA. Specifically, TRACE dynamically translates evolving reasoning paths into natural language narratives to maintain semantic continuity, while abstracting prior exploration trajectories into reusable experiential priors that capture recurring exploration patterns. A dualfeedback re-ranking mechanism further integrates contextual narratives with exploration priors to guide relation selection during reasoning. Extensive experiments on multiple KGQA benchmarks demonstrate that TRACE consistently outperforms state-of-the-art baselines.