Grant-Free (GF) access has been recognized as a promising candidate for Ultra-Reliable and Low-Latency Communications (URLLC). However, even with GF access, URLLC still may not effectively gain high reliability and millimeter-level latency, simultaneously. This is because the network load is typically time-varying and not known to the base station (BS), and thus, the resource allocated for GF access cannot well adapt to variations of the network load, resulting in low resource utilization efficiency under light network load and leading to severe collisions under heavy network load. To tackle this problem, we propose a multi-tier-driven computing framework and the associated algorithms for URLLC to support users with different QoS requirements. Especially, we concentrate on K - repetition GF access in light of its simplicity and well-balanced performance for practical systems. In particular, our framework consists of three tiers of computation, namely network-load learning, network-load prediction, and adaptive resource allocation. In the first tier, the BS can learn the network-load information from the states (success, collision, and idle) of random-access resources in terms of resource blocks (RB) and time slots. In the second tier, the network-load variation is effectively predicted based on estimation results from the first tier. Finally, in the third tier, by deriving and weighing the failure probabilities of different groups of users, their QoS requirements, and the predicted network loads, the BS is able to dynamically allocate sufficient resources accommodating the varying network loads. Simulation results show that our proposed approach can estimate the network load more accurately compared with the baseline schemes. Moreover, our adaptive resource allocation offers an effective way to enhance the QoS for different URLLC services, simultaneously.