Which plugin?

My site – https://haco.org.uk/ – has no access restrictions, ie the content is designed for both members and non-members of the association. However, I’d like to introduce a forum for association members only. Access applications would be referred to me so I could validate the applicant as an association member before approving.

I’ve looked at several plugins, installed a couple, uninstalled them when they weren’t quite right.

Please can you recommend plugins I should look at?