Considering network slicing in a cellular network, one of the most intriguing tasks is slice enforcement over air interfaces across multiple cells. The challenges lie in several aspects. First, resources allocated to different slices must achieve soft isolation at the link level. Second, users’ diverse QoS requirements must be satisfied even when communication links experience fading and interference. Third, long-term slicing policies must be conformed, no matter how unbalanced they are. To address these challenges, link-level slice enforcement is first formulated as a resource allocation problem that minimizes radio resource consumption while ensuring link-level soft slice isolation, guaranteeing users’ diverse QoS requirements, and conforming to slicing policies. Next, this problem is tackled via a deep reinforcement learning (DRL) based approach, through which LinkSlice is designed as an iterative two-stage algorithm. The first stage determines transmission rates for each link based on DRL. It is embedded with a graph neural network (GNN) to characterize link interference. Based on the transmission rates from the first stage, the second stage allocates resources to each slice. Performance results show that LinkSlice converges quickly to a near-optimal solution. It gracefully tackles the three challenges of link-level slice enforcement while further improving throughput by 18.5%.