Here are some steps for you:
1. Delete the old version of the app in your theme
2. Install app following link: https://apps.shopify.com/wishlist-compare
3. After searching the app, click the button Add App to start installing
4. You'll be moved to the Policy page, and then you need to accept the Privacy to complete the process. Now you successfully upgrade the app in your theme.
5. Since the app has been added to your theme, set those 2 blocks (Wishlist & Compare) to off mode at Show/Add Wishlist/Compare button rows.
Note: Installing the Wishlist Compare Plus doesn't affect the history in the operations of the old Wishlist Compare. However, in case you enter the store and realize the recent activities in the wishlist disappear after upgrading the app, please Reactive the app to bring the data back to your store.