Give the new date, and your preparation carries on, rescheduled around it.
If your exam date has not passed yet, change it as usual: in the app in Me under «Exam date», or on licento.com in your account.
If the date has passed and you did not sit the exam, because it was postponed, missed or moved by the authorities, tell us on licento.com in your account: open the exam under «Your exams», choose «Postponed» and give the new date. It changes nothing about your preparation; everything is rescheduled around the new date.
Until you tell us, nothing is scheduled for you: the examiner tells us nothing, and your plan stops on your exam date, never after it. A pass runs on its own dates, not on your exam's: if it ends before your new date, a new pass picks up where you left off.