Final answer:
The nurse promoting healthy coping skills for older adults previously hospitalized for severe depression is engaged in tertiary prevention, which helps manage long-term impacts of conditions and prevent progression.
Step-by-step explanation:
A nurse working on the promotion of healthy coping skills with older adult clients who had been hospitalized for severe depression and are now in a residential care facility is engaged in tertiary prevention. Tertiary prevention refers to actions taken to help prevent the progression of a disease or condition and manage its long-term impacts. In the context of mental health, particularly with individuals who have a history of severe depression, this would involve strategies like promoting healthy coping skills to manage stress and prevent relapses.