Final answer:
The nurse's priority action is to evaluate the client's nutritional status due to the presence of hematemesis and petechiae, which are urgent health concerns related to the client's anorexia nervosa.
Step-by-step explanation:
Based on the information provided, the nurse's priority action should be to evaluate the client's nutritional status. The client with anorexia nervosa has reported new onset of hematemesis, which is vomiting blood, a sign of potential gastrointestinal bleeding or injury likely due to induced vomiting. Additionally, the presence of petechiae on the face and sclera can be indicative of trauma from forceful vomiting. Assessments of the client's blood pressure and respiratory status, while pertinent, are less urgent in the context of the client's reported symptoms. Encouraging the client to continue therapy is important for long-term treatment but is not the immediate clinical priority given the acute physical findings.