Answer: It depends on what functionality you use to change/update the price.
If you change the price on a membership via the Pricing Options Bulk Management tool, the new price will only apply to new customers. Existing customers will keep on paying the price they were charged when they signed up.
If you are you using the Membership Fees Import/Export too, all customers currently on that membership will be charged the new price from the selected Active Start Date
Please refer to our Update a new price for new customers and Update Membership Fees for existing customers articles for guidance.