It is generally possible for you to give notice before the start of a new employment relationship so that you do not have to start the new job. However, this is only the case if you give notice in good time so that your notice period ends before your first day of work. However, if your notice period ends after the first working day, the employer can still insist that you work until the effective date of termination. However, you should take particular care to ensure that no corresponding contractual penalty clause has been included in your employment contract.