The Bible doesn't indicate that they would always have a king, but that the kingship would not depart from the tribe of Judah before Jesus/Shiloh was born. Herod was the first non-Jewish king to appear in Israel, and Jesus was born during his reign.

Genesis 49:10 The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be.