It depends on so many things that getting a straight answer is next to impossible.
- according to law, can a monarch be deposed legally, or must they die or relinquish the crown willingly for it to go to someone else ?
- what is the social and traditional view of elders - is it "the head of the family is always the elder", or is it something different, such as "the head of the family is the one in a position of power" ?
- are deceased people still part of the social order in some way or not ?
- what is the social view on resurrection ? what is the view of the law ? what is the view of the religion, or religions ?
- is the current monarch popular or not ? Was the deceased monarch popular or not ? How much time passed since their demise, and did their memory fade somewhat in the global consciousness ?
- would the current monarch defer to their ancestor, or are they secure enough in their own self ?
- are the people who want to resurrect the old king popular, or are they nobodies, or even considered troublemakers (or even criminals - you know, people who go looting ruins and tombs instead of earning their keep honestly with a trade) ?
- is the artifact known for this capability to design the rightful king ? Who actually believes that ? Who would use that legend to prop up their own candidate ? And if the artifact is not well known, can it be falsified somehow - use the legend to design a false artifact that would just convince the populace that whoever takes it *is* the rightful king ?
- is it possible to have several "rightful" kings ? (if there is no divine right, then it might be possible to have several legitimate kings and a partition of the kingdom).
The answer doesn't exist in a vacuum. You might get a civil war out of it, depending on the general population view of the matter and how the various political forces align with the crown contestants.
What is sure is that the *current* monarch starts with a position of power - they wear the crown, and if they want to keep it, someone will have to take it from them.