To be more precise, how to convey to readers that the king is under the law for it is the law that makes him king. His authority is executive and not legislative. Which does not mean that there's some legislature hanging about doing it instead. His place is to uphold the ancient laws and customs. Even if you manage to wiggle in a coronation in which he swears to do just that, it may go over readers' heads.
It certainly does for some because in the ever popular law that prevents the hero and heroine from marrying, you are bound to get the question why doesn't the king just change it if he seems the slightest degree favorable. Of course this also skips over the question of what the nobles and even the peasants or merchants will think if he does, but the assumption is that the king can, by definition, just snap his fingers and get it done.
A point not exactly clarified by writers who from Shakespeare onward have the kings refuse in the beginning and then do it at the end.
True, historically even kings bound by tradition would change the rules, but it was more likely to be under the pretext of codifying, or devising a legal fiction. Such as "disturbing the peace." This was originally a civil tort: you disturbed a man's peace, and he could sue you -- for more money the higher ranking he was. So the king dragged it into a crime to disturb the king's peace, and decreed that his peace -- the region the crime could occur in -- covered the kingdom. It might be interesting to see what a fictional king could whip up to explain away his law changes.