My iPad has iOS 10.3.3 and says no update available. How do I get it to update?

If your iPad is currently running, or cannot be updated beyond iOS 10.3.3/4, then you most likely have an iPad4.

Update support for iPad4 formally ended September 2017. The final iOS releases for this model were iOS 10.3.3 (WiFi Only models) and iOS 10.3.4 (WiFi & Cellular). iPad4 cannot be updated to any later major version of iOS as it lacks the minimum hardware requirements needed to run more recent versions.

Many App Developers have also dropped support for older devices and iOS versions preceding iOS12 - and have withdrawn older versions of their Apps from the Apple App Store. Withdrawal of Apps supporting older models of iPad is making their utility and usefulness significantly more limited.

If Apps that you need to use now have higher minimum iOS-version requirements, your only option is to replace your iPad with newer model. Even the basic current iPad7 supports current iPadOS 13.x - and has hardware specifications that will vastly outperform your old iPad4.

I hope this information is helpful - if only in clearly stating your current options.