In employment law you generally have a right to appeal any decision made at a disciplinary hearing. Your employer's written procedure may set out a time limit on any disciplinary appeal or it may be stated in the letter from your employer telling you the result of the first disciplinary hearing. You can meet the deadline by simply sending a letter stating you are intending to appeal and that you will supply the grounds of appeal later. If you have been dismissed then this is the time to seek some employment law advice.