'threaten a scandal" means that someone threatens to create a scandal (embarrassing situation) for you if you don't do what they want. For example, if an employee of a company knows that its president is having an affair with one of the other employees, he can threaten a scandal and demand money to keep quiet. We call this "hush money." "Hush" means to keep quiet.

If something or somebody threatens a scandal, it means that there is a possibility that something a person has done that is embarrassing or illegal will be made public. This could be something in the person's past, such as an affair or some crime they committed. "The senator's affair with a woman some years before threatened to become a major scandal and lower his chances to be re-elected." "The reporter threatened a scandal about the politician's criminal past if he did not get the whole story."