Eunice here from Shopify, thanks for posting!
I recommend getting in touch with the app's developers. They might be able to disconnect the app/s from their end and transfer them over to your new store. You will be able to find their contact details on their Shopify App Store listing, here is an example:
Or, contact details should be located on the third-party website you installed the app from. If they're not able to do that then I recommend contacting Shopify Support to discuss your options. While we’re not able to provide account-specific support via the Shopify Community at this time, we’d be happy to continue assisting you through live chat, email, or callback via the Shopify Help Center. This video clip shows you how to access the chat and email option. If you would prefer to speak with someone over the phone, please log in to your store when prompted to view the callback option. For the fastest support, I recommend selecting the chat option.
I hope this helps!