Are we going to get a Karna banner after Nightintale’s rate up or after Cū Alter’s banner?

I would say no. The next banner will be Queen Medb alone and after that, it will be Cu Alter. Karna will not have a rate up in this chapter like Tamamo and Jack in London.

Here's a list of JP banners:
http://fate-go.cirnopedia.org/summon.php
We are mostly following them step by step, so you can predict and plan quartz for over 2 year gap.