Can I update higher than 9.3.6 on ipad 3rd generation

You clearly have an iPad2, iPad3 or original iPad mini. These devices cannot be updated beyond iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular).

Apple formally ended update support for these devices in September 2016. None of these models can be updated to iOS 10 or later versions, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS.

Many App Developers have also dropped support for older devices and iOS versions preceding iOS11/12 - and have withdrawn older versions of their Apps from the Apple App Store, now limiting utility and usefulness of older devices. 

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 iPad model supports current iPadOS 13.x - and has hardware specifications that will vastly outperform your old iPad

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

Sorry no, because of hardware incompatibility.

Regards

Giulio

No, as I told you, it's a matter of hardware (RAM and/or other internal components) that do not meet the requirements for later iOS or iPadOS versions.

Sorry again.

Giulio