/api/v2/task_lists/{id}/reposition

Reorders a task list among the other task lists in its project. Pass move_before_id and/or move_after_id — the IDs of the task lists to position it relative to. When both are provided, the task list is placed between them.

{
  "data": {
    "type": "task_lists",
    "attributes": { "move_after_id": 7740 }
  }
}