If you update a membership plan, those changes will not be applied to any existing client's memberships with that plan automatically. If you want to update those, that has to be done for each of the client's memberships individually.
Here's how it looks if a client's membership is outdated.
On the Membership Details window, select Show details or upgrade.
Review the details and Switch.
Select Options on Membership's Screen.
Toggle "Show different versions only" and Apply.
Note: When a client's membership is switched to the current version of a membership plan:
Any product or service discount percentage change takes effect immediately
Any price or included services changes will take effect with the next membership payment at the start of the next billing cycle