Final answer:
The nurse should first complete a neurovascular assessment of the right hand before taking further actions, to evaluate circulation and nerve function to the limb.
Step-by-step explanation:
A nurse who is unable to palpate a client's right radial pulse four hours after surgical repair of a compound fracture of the right ulna should first complete a neurovascular assessment of the right hand. This initial step is crucial because it provides a comprehensive evaluation of not only the pulse but also motor and sensory function, skin temperature, and capillary refill, which together can indicate whether the blood flow and nerve function to the limb are intact or compromised. If any abnormalities are found, the healthcare provider should be notified immediately. Elevating the client's right hand may be helpful to decrease swelling and improve blood flow, but it is not the immediate first action before assessing the extent of the problem. Similarly, measuring blood pressure and apical pulse rate, while important, are not as directly related to the assessment of the blood flow to the affected extremity as a neurovascular assessment.