In a nutshell
A DPB is an organization in the UK that is designated by the Treasury to regulate the activities of member firms of profession such as solicitors, accountants, and chartered surveyors.
Member firms that belong to a DPB are permitted to carry out a limited range of regulated activities (also known as exempt regulated activities), without needing to obtain direct authorization from the Financial Conduct Authority. The activities must be incidental to the business’s core activities.
See here for the list of designated professional bodies in the UK.