The primary nursing intervention for a client with a C-3–4 fracture is airway assessment and stabilization. This is because cervical spine injuries at this level can compromise the airway, leading to inadequate ventilation. Ensuring the airway is open and stable is the most critical initial step in managing such injuries. While other interventions such as stabilization of the cervical spine, confirmation of spinal cord injury, and normalization of intravascular volume are important, they are secondary to ensuring the airway is secure and the patient is ventilated adequately.