Hi

The current YouTube App requires iOS12 or later. If your iPad is currently running, or cannot be updated beyond iOS 10.3.3/4, then have an iPad4.

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 The 32-bit platform upon which the iPad4 is based is obsolete.

Most App Developers have dropped support for 32-bit devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store.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 Once compatible versions Apps are withdrawn, you’ll not be able (re)download or (re)install them.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 than your iPad can supprt, your only option is to replace your iPad with newer model. Of current models, even the entry-level iPad9 supports current iPadOS 15 - and has hardware specifications and capabilities that vastly outperform your old iPad4.

For YouTube, while you are unable to install the YouTube App on your iPad, YouTube can be accessed using a web-browser - although the browser itself must still be supported by the YouTube web-service.

You can't.

You need to use the YouTube Website in a Web browser instead, and login into your YouTube account that way.