To guarantee the safety and smooth control of Unmanned Aerial Vehicle (UAV) operation, the new control and command (C&C) data type imposes stringent quality of service (QoS) requirements on the cellular network. However, the existing bit-oriented communication framework is already approaching the Shannon capacity limit, which can hardly guarantee the ultra-reliable low latency communications (URLLC) service for C&C transmission. To solve the problem, task-oriented semantics-aware (TOSA) communication has been proposed recently by jointly exploiting the context of data and its importance to the UAV control task. However, to the best of our knowledge, an explicit and systematic TOSA communication framework for emerging C&C data type remains unknown. Therefore, in this paper, we propose a TOSA communication framework for C&C transmission and define its value of information based on both the similarity and age of information (AoI) of C&C signals. We also propose a deep reinforcement learning (DRL) algorithm to maximize the TOSA information. Last but not least, we present the simulation results to validate the effectiveness of our proposed TOSA communication framework.