It's not possible to join the Professional DJ team and Cloud Option DJ team in any of the following cases:
・The Dropbox account you are using is a team account.
・You created your Dropbox account via "Sign in with Apple ID".

If either of the above applies to you, you'll need to create a new Dropbox personal account. If you're already using Cloud Library Sync, move your music files to the new Dropbox account.
Find details here.

If you don't receive an email from Dropbox inviting you to join the Professional DJ team/Cloud Option DJ team, check your spam folder.
If you didn't receive the email, you can also receive an invitation to join the Professional DJ team/Cloud Option DJ team from the notifications on the Dropbox website.

Find more information on how to check your notifications here.