Final answer:
The nurse should first investigate the potential lack of adherence to prescribed drug therapy to understand why the client's hypertension has not improved.
Step-by-step explanation:
When assessing a client whose hypertension has not improved, a nurse should first explore the possibility of lack of adherence to prescribed drug therapy. This is a common issue that can significantly impact blood pressure control and can be due to various reasons such as forgetfulness, side effects, or misunderstanding the dosage instructions. Before considering potential medication interactions, heavy alcohol use, or progressive target organ damage, it is essential to ensure that the patient has been consistently following the treatment plan. This is because non-adherence immediately impacts blood pressure management and is often an easily modifiable factor.