You may have received an email from Dropbox recently encouraging you to upgrade to a paid plan. Pay close attention to the wording here. "No new devices" doesn't mean anything is currently wrong. They are hoping you will upgrade to a paid plan.
This is unfortunate. This new as of March. Dropbox, in a hope to push subscriptions are now limiting basic user’s accounts to only 3 devices. If you’d like to access your dropbox files from more than three, you’d need to upgrade to a paid plan. So the question becomes, do you need access on more than 3 devices? Probably not. iPhone, iPad, laptop. I’d say don’t upgrade until a more compelling reason reveals itself.