With iPadOS 15.8.3 installed, you presumably have either an iPad Air2 or iPad mini4 - neither of which support iPadOS 16.x or later.
If you need to use Apps that require a higher version of iPadOS than your iPad is capable of support, you have no alternative other than to replace your existing iPad with a much newer or current model iPad.
For information, here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:
32-bit devices (obsolete)
iPad1 - iOS 5.1.1
iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi+Cellular)
iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi+Cellular)
64-bit devices
iPad Air1*, iPad mini2 and iPad mini3* - iOS 12.5.7
iPad Air2, iPad mini4 - iPadOS 15.8.3
iPad5, iPad Pro (9.7"/12.9" first generation) - iPadOS 16.7.10
(*) obsolete
Newer models are all able to be updated to the current version - iPadOS 17.6.1
- iPad Pro 13" (M4)
- iPad Pro 12.9" (2nd generation and later)
- iPad Pro 11" (1st generation and later + M4)
- iPad Pro 10.5"
- iPad Air (3rd generation and later + M2)
- iPad (6th generation and later)
- iPad mini (5th generation and later)