You linked your tasks, but now the successor task doesn't move.
There may be several causes:
If a task has any actuals applied, such as an actual start date or a percentage of work completed, the task can't be rescheduled any earlier than the date when the task actually began. If no progress is entered and the task has an inflexible constraint, the constraint can take precedence over task dependencies.
For example, if a task has a Start No Earlier Than (SNET) constraint set to July 1, the task is tied to that date and won't be rescheduled to an earlier date, even if its predecessor finishes on June 28 and the successor task could start earlier than July 1.
In Project, if you create a task by dragging the pointer on the chart portion of a Gantt Chart view, a Start No Earlier Than (SNET) constraint is set on the task for projects that are scheduled from the start date. For projects that are scheduled from a finish date, a Finish No Later Than (FNLT) constraint is set on the task.
If the successor task is completed, it will not move to reflect the link.
If you set Calculation mode for your project to Manual, the successor task will not move.
To reset the task constraint to be more flexible, click the task, click Task Information , and then click the Advanced tab. In the Constraint type list, click As Soon As Possible. Project then schedules the task's start date according to the task dependency.
To make task dependencies override inflexible constraints for all tasks, on the Tools menu, click Options, and then click the Schedule tab. In the Scheduling options section, clear the Tasks will always honor their constraint dates check box.
To set calculations to automatic, on the Tools menu, click Options, and then click the Calculation tab. In the Calculation options for Microsoft Office Project section, next to Calculation mode, click Manual.