Tim Drake should become a traveling detective, helping other heroes with cases in their respective cities (personal idea)
Tim has kinda felt displaced for quite a while since the introduction of Damian. And now he's quit as Robin all bets are off for what'll happen next.
I'd say his most defining traits as a character are his intelligence, detective skills and the fact he actively sought out becoming a Robin. So I'd say him leaving Gotham and becoming a traveling hero that handles large conspiracies, helping out other superheroes with tricky cases in their city, would be a fitting evolution.
I know a lot of people aren't a fan of the Red Robin alias but I don't think it's bad at all. The name would also illude to the idea that he's still helping another hero like he was as Robin. I do think he may need a more iconic redesign that properly conveys his role and his intelligence without getting rid of the current defining features.
As for how he could transition back into vigilantism, I have no idea. Maybe he slowly grows bored living out his happily ever after with Bernard causing him to seek out needless mysteries which slowly spirals into him leaving.