Moving a member between memberships works for one-time (seasonal) memberships. Recurring memberships are tied to the customer's own subscription, so an admin can't reassign those.
Go to Customers, search for the customer, and click their name to open their customer card. In the Memberships section, cancel the old membership and add the new one. For recurring memberships that need to stop renewing, use Cancel membership and pick whether benefits should end now or at the end of the paid period. See How can I cancel a membership.