Final answer:
The priority nursing action after inserting a right subclavian central venous access device is to obtain a chest x-ray to determine placement.
Step-by-step explanation:
The priority nursing action immediately after insertion of a right subclavian central venous access device is to obtain a chest x-ray to determine placement. This is important because it ensures that the catheter is properly positioned in the subclavian vein and not causing any complications. Auscultating the lungs, drawing a blood sample to assess blood glucose level, and assessing the right upper extremity for neurologic deficits are important nursing actions but not the immediate priority after the insertion of the catheter.