The anger of Balak would most probably have broken out in some act of violence upon Balaam's person, had he not been restrained by fear. And it is likely that, as the LORD had yet more prophecies to be delivered upon this occasion by Balaam, the LORD over-ruled the mind of the prince of Moab, that he should not.
Related Commentaries of Numbers 24:10
Numbers 24:10-11
10 And Balak's anger was kindled against Balaam, and he smote his hands together: and Balak said unto Balaam, I called thee to curse mine enemies, and, behold, thou hast altogether blessed them these three times.
11 Therefore now flee thou to thy place: I thought to promote thee unto great honour; but, lo, the LORD hath kept thee back from honour.