I'd like to move my village closer to the King I'm following but is it possible to move in the first place?
No, it's not possible.
The only option you could follow would be the relocation of your village, but it'd require you to have twice the population of your king (and not only that).
As Knud already mentioned, that is unfortunately not possible. It’s a question of luck whether you get to have a good king when you start your game as a governor, or vice versa, whether you get to have good governors when you start as a king. If you’re dealt a bad hand, your king is an absolute beginner or the governors’ villages are more like towns.
Requirement for relocation: You only have one village and you have at least twice as many inhabitants as your current king.
As soon as the requirements are satisfied, you will be offered two kingdoms in your area, whose kings have more than 50% of your inhabitants and who have been online within the last 24 hours.
Requirement for relocation: You only have one village and no active governors in your kingdom.
As soon as the requirements are satisfied, you will be shown two kingdoms in your area, whose kings are inactive since at least 24 hours, but that have active governors. If you confirm the resettlement, you will swap places with the inactive king.
Beware, inactive Kings are often inactive because other Kings/Dukes around them are wanting them out, and they are being farmed and catted, I don't recommend teleporting as a King, you are extremely likely to end up wishing you had remained where you were.
If a king is thinking of teleporting, then that player probably shouldn't be a king in the first place.