The rapid growth of large language model (LLM) inference services has increased the demand for efficient multi-tenant GPU scheduling. While modern inference runtimes such as vLLM improve throughput through continuous batching and optimized memory management, accurately estimating the runtime cost of heterogeneous inference requests remains a significant challenge. In practice, observed output lengths often deviate from admission-time estimates, creating runtime token drift that can lead to workload misclassification, queue imbalance, increased tail latency, and degraded Quality-of-Service (QoS). This paper presents DriftSched, an adaptive QoS-aware scheduling framework for multi-tenant LLM inference serving on NVIDIA L4 GPUs. DriftSched combines workload classification, token-budget estimation, tenant-aware queue management, and runtime feedback-driven drift compensation to improve admission-time scheduling decisions. The framework evaluates FIFO, Priority, Weighted, Shortest-Job-First (SJF), and Aging Priority scheduling policies under heterogeneous multi-tenant workloads. Experimental results demonstrate measurable runtime token drift across workload categories. Adaptive bias correction reduces workload estimation error by an average of 38.8% (MAE) and 40.5% (RMSE), improving workload classification stability and scheduling accuracy. Among all evaluated schedulers, SJF achieves the best overall performance, reducing median end-to-end latency by approximately 42% and P99 latency by approximately 16% relative to FIFO under sustained GPU contention. The work contributes an adaptive drift-aware scheduling architecture, a runtime token-drift compensation mechanism, and a reproducible benchmarking framework for evaluating QoS-aware LLM inference scheduling on shared GPU infrastructure.