Can I use my old wired ear buds with my new iPad?

Yes, but you will need an appropriate adapter suitable for your iPad:

For an iPad with a Lightning connector:

• Lightning to 3.5mm Headphone Jack Adapter

https://store.apple.com/uk/xc/product/MMX62ZM/A

For a 2020 iPad Air4 - or 2018/2020/2021 model of iPad Pro:

• USB-C to 3.5mm Headphone Jack Adapter

https://store.apple.com/uk/xc/product/MU7E2ZM/A

if the connector fits sure, you can also use headsets not made by apple if the connector fits