In general, there is no obligation for an employer to offer an appeal but, if a case ends up going to an Employment Tribunal, in certain scenarios you can be penalised for failing to provide the right of appeal.
Always check your handbook for employees and follow the grievance procedure it sets out. If this does not exist or fails to deal with appeals, follow the Acas Code of Practice (except in cases of redundancy or the non-renewal of fixed term contracts on their expiry, where it does not apply).
If you receive an appeal request, you should arrange an appeal hearing without unreasonable delay, generally within five working days. When writing to the employee to confirm the hearing, also remind them of their right to bring a companion; this can be a colleague or trade union rep. The appeal hearing should generally be held in a similar way to the initial hearing; however, if possible, a more senior manager should handle the appeal hearing - or at least a different manager to the one who handled the initial hearing.
Communicate the outcome of the appeal hearing to the employee in writing as soon as possible, preferably within 24 hours.