How to update third gen I pad to iOS 13

If you have iOS 10.3.3 or iOS 10.3.4 for cellular models then

you have an iPad 4th generation not a 3rd generation as you said.

To be sure tell us what you see in

Settings > General > About > Model Number > tap here and tell us the number starting with A????

You can’t update it. The 3rd gen iPad has reached the end of its update life. The internal hardware cannot handle the newer operating systems.

If you need iOS 13+ (14 will be out in the next month or two most likely) then you need a newer device.

Simple answer is you don't, because you cannot update a 3rd generation iPad at all. It is now too old, too under powered, no longer supported and completely incapable of running the now required 64 bit software for the newer iOS levels.

Your iPad is now 8 years old. It has past its prime and then some. If you need the newer iOS levels, because most apps are no longer compatible with such an out of date device, then it's to buy a newer more modern iPad.

Sorry.

If your iPad is currently running, or cannot be updated beyond iOS 10.3.3/4, then have an iPad4. An iPad3 is similarly limited, but can only reach iOS 9.3.5/6.

Update support for iPad4 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. The 32-bit platform upon which the iPad4 is based is effectively obsolete.

Many App Developers have also dropped support for older devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store.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. Once compatible versions Apps are withdrawn, you’ll not be able (re)download or (re)install them.

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 and capabilities that will vastly outperform your old iPad4.

I hope this information is helpful - if only in clearly stating the limitations of your iPad4 and your available options.

You can’t. You need at least the iPad (5th generation), iPad Air 2, iPad mini 4, and all iPad Pro models.