Succession planning permissions control how users can interact with the Succession Org Chart. Permissions are defined from Manage Permission Roles in the Succession Planners section.

Successors, like other configured fields for the incumbent, are visible for an org chart node based on the target population defined for the Succession Management and Matrix Report Permissions. The Succession Planning Permission allows users to nominate successors for their target population. The final piece is to grant access to the org chart itself using the Succession Org Chart Permission.
If your solution includes the approval process for nominations, pending nominations are not visible to users who only have the Succession Management and Matrix Report Permissions assigned to them. They also need the Succession Planning Permission assigned.
Additional details regarding Succession permissions are available in Succeeding as a Consultant.