Leadership succession occurs regardless of demographic shifts. Nonprofits that are serious about their own sustainability will also be serious about planning for smooth and thoughtful leadership successions. Planning for leadership succession should take into consideration not only planned transitions but also unplanned ones -- whether for staff or board leaders -- and sustainability also means cross-training staff so that important day-to-day functions will continue uninterrupted. Who is responsible for all this planning? The board development committee or "board governance" committee will generally focus on leadership succession at the board level, while staff is charged with identifying transition plans for staff leadership succession, whether planned or unexpected. However, because the board is ultimately responsible for oversight of the executive director, the board's involvement in succession planning for the executive director is crucial. 
From the National Council of Nonprofits:
Succession Planning includes:
- Identifying current challenges and those that lie ahead, and the corresponding leadership qualities that are needed to navigate these challenges successfully.
- Drafting a timeline for leadership successions that are planned.
- Creating an Emergency Succession Plan to address the timely delegation of duties and authority when there is an unexpected transition of leadership.
- Identifying leadership development opportunities for staff and board members to expand their leadership skills so that the organization will have a "deeper bench" of future leaders.
- Cross-training current staff to minimize the disruption from unexpected staffing changes.
- Making plans to adequately support newly placed employees, such as with coaching.
- Identifying how your organization will communicate with stakeholders before, during, and after a transition of leadership.
Resources & Sample Documents
National Council of Nonprofits: Succession Planning for Nonprofits - Managing Leadership Transitions
BoardEffect: Succession Planning for Nonprofit Organizations
Anne E. Casey Foundation (AECF): Building Leaderful Organizations: Succession Planning for Nonprofits
Anne E. Casey Foundation (AECF): Executive Transition Series
NonprofitAF: 10 Steps for a Kick-Ass Emergency Succession Plan
BlueAvocado: Succession Planning for Nonprofits of All Sizes
Society for Human Resource Management: Developing Leadership Talent - A Guide to Succession Planning and Leadership Development (pdf)
National Council of Nonprofits: Investing in Leadership