Yes, a track bar in Gantt chart view allows you to set or adjust the start/due date on your card. Simply click on the left/right edge of the track bar representing the time frame for a particular task and drag it to a particular date. Dates will change automatically. If you have pushed them to your Google Calendar, changes will be displayed there as well.
Alternatively, click on the card in Gantt chart view to open the right panel and set new start/due dates manually in the Card Details section.