The admin tool setting mentioned here will force the client to the subscription purchase process when trying to do anything on the site…as well as push them into subscription purchase after registration.

After turning in on, any logged-in user who is in a subscription-based User Group but does not have an active subscription will be automatically redirected to the "Purchase/Extend Subscription" page from any other page in the software. There are a few logical exceptions, such to the forwarding like the login/logout processes, the front page, the Cart and transaction processing (The latter two are where subscription purchase happens).

Since users are automatically logged in as part of a completed registration, this can be used to append the Purchase Subscription process to the registration workflow.

Look to the following admin tool setting:

Addons > Subscription Pricing > Settings > Require all registered users to have an active subscription before accessing any pages