Hi Jul!
As @DonaldH said you can use Discourse to have a forum like this one but you will need to self host on a separate droplet or pay a substantial amount each month.
Last week I worked on an integration called Atrium which lets you create a forum natively using Ghost’s membership features. I talked about it here 
This would let you filter which members could contribute to content on your site so you can do as you suggest and only let your paid members be part of the community.
All without using and hosting a separate service like Discourse.
Atrium is in early access right now and there are lots that could be added so I’d love to have a quick chat to see if it can fit your use case!
If you like the sound of it please drop me a message on here or DM me on Twitter 