There are several ways to achieve this, one simple way is to add a Task under the Ticket and set its due date to 7 days. Then, when the Task is due follow up with the customer. To add a Task simply select the New Task option from the Ticket Window, either under the More Actions dropdown on the toolbar, the New Task option in the Preview page or the Pending tab. Besides, you may want to use
Activity Templates for Tickets and configure the one, or more, follow tasks. Then, when you apply an Activity Template to a Ticket it will automatically add all entries, for example, will add a Task and it'll calculate the Due Date automatically as per the template settings.
Hope this helps.