As the landscape of online social networks continues to evolve, the task of expanding connections and uncovering novel relationships presents a growing complexity. Link prediction emerges as a crucial strategy, harnessing the current network dynamics to forecast future interactions among users. While traditional single-layer network link prediction models boast a storied legacy, recent attention has shifted towards tackling analogous challenges within the realm of multilayer networks. This paradigm shift underscores the critical role of extracting topological and multimodal features to effectively evaluate link weights, thereby enriching link prediction within weighted networks. Furthermore, the establishment of trustworthy pathways between users emerges as a pivotal tactic for translating unweighted similarities into meaningful weighted metrics. Leveraging the foundational principles of local random walk techniques, this paper introduces the trustworthy Lévy-flight semi-local (TLFSL) random walk framework for link prediction in multilayer social networks. By seamlessly integrating intralayer and interlayer information, TLFSL harnesses a dependable Lévy-flight random walk mechanism to anticipate new links within target layers of multilayer networks. Traditional local random walk techniques often overlook global relationships, as they confine path exploration to immediate neighbours. However, the absence of a direct edge between nodes does not necessarily imply a lack of relationship; nodes with semantic affinity may be spatially distant within the network. To overcome this limitation, we introduce the concept of semi-local random walk, which enables walker hopping with a wider global perspective. Meanwhile, TLFSL includes a distributed local community detection strategy to improve the performance of TLFSL in dealing with large-scale networks. Rigorous experimentation across diverse real-world multilayer networks consistently demonstrates TLFSL's superior performance compared to equivalent methods. © The Author 2024.