Vehicular ad hoc networks (VANETs) provide a robust infrastructure for intelligent transportation system (ITS) applications. VANET communication involves vehicle-to-vehicle and vehicle-to-infrastructure connections, primarily with roadside units (RSUs). Analyzing cognitive radio (CR)-VANET studies revealed two key performance issues: high energy consumption and latency. To address these challenges, we propose a novel approach: link stability and mobility prediction-based clustered CR-VANETs, known as LMCCR-VANET. LMCCR-VANET consists of four main components: CR-VANET construction, clustering model, speed-based mobility prediction, and link-based multipath routing. Initially, we establish cluster-based CR-VANETs to analyze and mitigate spectrum scarcity and power utilization problems in VANETs. Mobility prediction evaluates vehicle speed variations and predictions. Finally, employing link stability-based multipath routing (LSMR) in conjunction with the fuzzy interference model and ad hoc on-demand multipath distance vector (AOMDV) routing protocol ensures stable and efficient routing. Experimental results showcase the superiority of LMCCR-VANET. It exhibits enhanced energy efficiency, delivery rates, reduced energy consumption, end-to-end latency, and routing overhead when compared to recent works such as SCCR-VANET, CFCR-VANET, and MMCR-VANET.