It is not very wise to make a king angry - unless it is a command from God that you speak in this way. Proverbs was written in the time when kings ruled over the land and their word was law. In some kingdoms a king could put anyone he wanted to death for any reason that he desired. This is why we are being advised not to provoke a king to anger.
When I read about the "terror of a king" I think of the book of Esther and the fabled anger of king Ahasuerus. This kind was known for his anger. When he became angry the phrase "heads will roll" was more than just a phrase. He became angry with his wife and deposed her from the throne. So there was no one out of his reach. In this situation it was extremely unwise to make this man angry. That was why Esther was hesitant to come before him without being asked to appear. His anger was so dangerous that a law was put into place that anyone who did this would be put to death unless the king extended his golden scepter to that person. It wouldn't take long to realize that nobody wanted to bother the king - and those who did - might not live very long to tell of it. Yet God needed Esther to come and plead for her people. She risked the anger of her king and was delivered by the Lord because of it. Not as much could be said for Haman - whose plot, once revealed made the king leave a banquet in anger. When he returned, Haman was begging for his life while falling at the couch of Esther. When the king saw this - he saw it as Haman assaulting her - and his fury rose. As the word went forth from his mouth - Haman's head was covered with a black hood - and not much more than moments later he was hanged at the gallows he intended for someone else. Definitely we see here that the anger of the king, when provoked, will cause a man to forfeit his life.
There is a principle here that can go beyond just relationships with kings and royalty. It has to do with how we speak and treat our boss in life. The boss-man has the power - and that power can mean you have a job or you don't have one. So speak with respect and with deference to a person in high levels of authority. Their anger is not like a normal person's anger. They have power and authority and when angry can use that authority to punish whoever it ticking them off. So . . . act with resepct and with reverence to those in authority. Show them respect and treat them as the position deserves. To do otherwise might cost you more than you think.