Final answer:
The nurse should instruct the client to notify their provider if they experience a persistent cough as an adverse effect of the ACE inhibitor medication.
Step-by-step explanation:
When teaching a client who has a new prescription for an ACE inhibitor to treat hypertension, the nurse should instruct the client to notify their provider if they experience a persistent cough as an adverse effect of this medication. ACE inhibitors are known to commonly cause a persistent cough, which can indicate a potential side effect and may require a medication adjustment or alternative treatment.