You have to fully exit the mission/patrol by clicking 'return to base' and going back to the campaign menu. Click on the desk in the office screen to see the patrol logs and career history to see that Patrol 1 has been completed. Click the large map on the wall to begin next patrol. Usually you'll be given new objectives but not always.
Also a good idea to watch the fuel supply to ensure you have enough remaining to get back to where you started. The navigator officer can give some advice on this. Lower speed settings are more economical. Good hunting.
