How to install apps on iPad 4 which require IOS version 11 or higher?
Answer is No, you can't do it. However, there are few workarounds and one I did a bit long time was: 


You need to have a newer iOS device (if you do not have one, you can borrow one from a friend).
Make sure that you’re signed in to iCloud with the same Apple ID on both devices (if you are borrowing a device from a friend, your friend needs to log out first, your friend may want to make copies of the information that he stored in iCloud).
On your new device, launch the App Store and find the app and download and install it.
Now get the old device that you want to install the app. On your old device, go to App Store and then Purchased. You will see the app there because you just purchased it. İf you do not see it yet, just wait.


And then tap the iCloud icon to download the app.
And the download will start.


Note that these methods may not work for all apps. This only works if the developer of the app had not deleted it from Apple’s App servers. Furthermore, since you are downloading an older version of the app, it is highly likely that not all features of the app may be available.