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You have two approaches to achieve this.
The first is the one you have done, only you must first activate the automation in the new track. Then the .mid automation file will be created. Now, delete the new one and rename the old one as the new one.

The second thing is to leave the old clip. Open its properties and replace the old wav with the new one.
The second approach is better, because if there are multiple automations it keeps them all.