It is important for elders to consider the continuity of leadership that lasts beyond their lifetime.
The concept of transitioning leaders is biblical: we see many examples of leaders training future leaders, including Paul, Timothy, and even Jesus himself. Jesus did not wait till the end of his earthly ministry before looking for those who would continue the work that he started. He recruited them early in his ministry and trained them specifically.
Join Alex Strauch and Dave Anderson for this series on transitioning elders.
18 Words for New Elders. Excellent article for new (and long standing) elders, summary advice from a variety of experienced elders.