Final answer:
The nurse should perform a priority assessment of the client's level of consciousness in a case of third-degree heart block.
Step-by-step explanation:
The priority assessment that the nurse performs for a client with third-degree heart block is level of consciousness. Third-degree heart block is a condition where there is no correlation between atrial activity (the P wave) and ventricular activity (the QRS complex). In this case, the heart rate is slow at 35 beats per minute, which can lead to decreased cardiac output and potential hypoperfusion to the brain. Therefore, assessing the client's level of consciousness is important to monitor for any signs of cerebral hypoperfusion or decreased perfusion to other vital organs.