Extract WhatsApp Backup
Introduction
The problem lies with the fact that WhatsApp does not store a history of your chats on its servers (except undelivered ones). That means that unlike other messaging providers, WhatsApp cannot simply repopulate your chat history on every device because there is no central location (server) that stores them for you. While this is a great step towards privatizing your chats, this makes things all the more difficult for your case.

Analysis  


In early 2017, WhatsApp has encrypted its backups to iCloud, which means that if you lost your iPhone prior to
this, you may (optimistically) be able to read them in plain text.
This would probably require you to connect the iPhone via cable to a
third-party app on your Mac/PC like iPhone Explorer or
iExplorer. I used these years ago to extract files hidden in
the file system of an old iPhone 4. But I think it is saved to say
that there is absolutely no guarantee that you will even be able to
open any WhatsApp files you may find (due to encryption).
It seems to be entirely possible, however, to restore your current iPhone from the backup of the old one and view your messages that way. For what its worth, you are better off not risking your current chat threads, so do a backup of your current state. Therefore you can always restore it to today's version if things start to go wrong.
You may be interested in this article which discusses ways to transfer chat histories to other phones (Android, in case you switched to one - you didn't mention).


Conclusion
Based on the (limited) options available to you, I'd recommend trying the second one first as you will have the greatest chance of actually reading the messages, compared to option one and three. Please read through this guide to learn how to restore your chat history. I am interested if it works for you. Let me know how you get on.