A sensing-aided covert communication network empowered by pinching antenna systems (PASS) is proposed in this work. Unlike conventional fixed-position MIMO arrays, PASS dynamically reconfigures its pinching antennas (PAs) closer to the legitimate user, substantially enhancing covertness. To further secure the adversary's channel state information (CSI), a sensing function is leveraged to track the malicious warden's movements. In particular, this paper first proposes an extended Kalman filter (EKF) based approach to fulfilling the tracking function. Building on this, a covert communication problem is formulated with a joint design of beamforming, artificial noise (AN) signals, and the position of PAs. Then, the beamforming and AN design subproblems are resolved jointly with a subspace approach, while the PA position optimization subproblem is handled by a deep reinforcement learning (DRL) approach by treating the evolution of the warden's mobility status as a temporally corrected process. Numerical results are presented and demonstrate that: i) the EKF approach can accurately track the warden's CSI with low complexity, ii) the effectiveness of the proposed solution is verified by its outperformance over the greedy and searching-based benchmarks, and iii) with new design degrees of freedom (DoFs), the performance of PASS is superior to the conventional fully-digital MIMO systems.