When you want to change the price of a already used plan variant, this will affect all of your customers already using this plan variant and all new customers.
So it might be a good choice, to create a new plan variant with the new plan for all new customers and to keep the old plan variant with the old price separately. Your old customers can be migrated via the "Up-/Downgrade" menu over time to the new plan variant, if you wish.
For an existing customer, the price change will be used for the next billing. If you are changing the contact in the past for an existing customer, the new price will be used for the time that you are changing.