While Lord Sugar presents The Apprentice series on the BBC he is primarily a businessman and he isn’t a BBC staff member. 

The BBC’s Editorial Guidelines contain advice about the external activities of freelance presenters. They explain that the constraints for a freelance presenter are not the same as they are for say a BBC News or Current Affairs presenter. 

However in the light of recent events the BBC’s Director General, Tim Davie, has announced an independent review of the BBC’s guidance in this area, namely the BBC’s existing social media guidance, with a particular focus on how it applies to freelancers outside of news and current affairs.