Can I apply for a further extension of stay in Thailand after renewing my passport while on an OA visa?

You would not have any problem applying for a new yearly extension with your new passport as long as you meet the requirements.

When you receive your new passport, bring old and new passports and the letter the embassy issues to the Immigration office, then apply for transfer stamps. Then you will be fine for new extension applications in the future. There is no limitation on how many times you can apply for a long-term extension.

But remember, even you change to your new passport, your stamps are linked to your original Non-OA entry stamp, which means you need to keep meeting the requirement for yearly extension from Non-OA.