Final answer:
A perimenopausal client on hormone replacement therapy should be instructed to notify their provider immediately if they experience chest pain, as it could indicate a serious cardiovascular event.
Step-by-step explanation:
For a perimenopausal client with a prescription for hormone replacement therapy (HRT), the nurse should instruct the client to notify the provider if they experience chest pain. This symptom could indicate a serious adverse effect such as an increased risk of heart attack or other cardiovascular issues, which is a known risk associated with HRT. The other options, such as weight loss, mood swings, and visual disturbances, while they may be concerning and warrant a discussion with a healthcare provider, are not typically as immediately life-threatening as chest pain.