Pinion gearbox + Gates belt drive - what are my options for 36-hole rear hubs?
Hope Pro 4 Trial/Singlespeed Hub is available in 36 hole configuration.

Here is a link to the product page:
https://www.hopetech.com/product/pro-4-trialssingle-speed-rear-hub/

You should be able to source them through your local bike dealer or via the internet. The are available for quick release and 12mm axles so you should be able to fit them to your new frame.