WARNING: The following article contains spoilers for I Am Batman #1, available now from DC Comics.
The structure of the Bat-Family has never been definitive. There have, of course, always been mainstays who remain a part of the main group. Batman, his Robins, Barbara Gordon, and Alfred have always been present in some shape or form. But beyond that, the roster has always been in a state of flux. Even by their standards though, the Bat-Family has rarely been in a stranger place than they are right now. Alfred is dead, Bruce Wayne is set to leave Gotham soon, even Dick and Damian have left the city.
But new heroes are rising, most prominently Jace Fox, the new Batman. He is a very different sort of vigilante from Bruce, however, and how he fits into the Bat-Family, if at all, might not just change the leadership of the group, but how they choose to operate.
Jace Fox is the eldest son of Lucius Fox. Formerly known as Tim Fox, he debuted in Len Wein and Irv Novick's Batman #101, having been called back to the city by his father after being absent for many years. Tim had been responsible for killing a man while driving, and it was only thanks to his parents' influence that he avoided facing the penalties. The experience deeply affected Tim, seeing how the privileged can rig the system against those with fewer means than them. He spent the next few years training to be a martial artist and strategist, adopting the new name "Jace"
Since returning to Gotham, Jace has discovered his father's link to Batman, but not the true nature of his family's relationship with the Dark Knight. In I Am Batman #1 (by John Ridley, Olivier Coipel, Alex Sinclair and ALW's Troy Peteri) he has since decided to co-opt the Batman symbol for himself, intending to transform it into something the people can believe in again. The way he sees Batman right now is as a tool for the elite of the city, namely Bruce Wayne and Lucius Fox. He believes that Batman has distanced himself from the very people he originally set out to protect, becoming nothing more than an empty promise and a way for the rich to benefit from having a super-soldier on the streets.
To that end he has taken to being more street-level than Batman has been in years, distancing himself from the rest of the Bat-Family as he strikes out on his own. In this way, Jace doesn't just intend to fight villains, but the system that helped spawn them, namely the corruption in Gotham. Like Bruce did all those years ago, Jace became Batman to put the privileged few on notice and make sure that they faced consequences when they did wrong.
So where does that put him in the Bat-Family's structure? The most likely answer is that he doesn't really fit at the moment. Jace's attitude is one of an outsider. He has his own support system and resources and his more aggressive attitude when handling criminals makes him more similar to Red Hood than Batman. Then there is the simple fact that the Bat-Family, by virtue of being trained by the original Batman, is not looked upon favorably by Jace.
There is evidence to support this. In Future State, Jace never opted to interact with the Bat-Family for years. So much so that they still have no idea who he really is, even if they are aware of him. But if he did try to join the group, as mentioned above, he might find more in common with Red Hood than the others. Each of the Bat-Family has tried to make the world a better place in their own way, but Jace is more aggressive in his attempts, not content to work within the system if it's broken. He'd rather fight it completely to bring about the change he seeks.
That might ruffle some feathers, but honestly, Jason has probably done a lot worse and he's still allowed to patrol Gotham. Jace could become a member of the Bat-Family willing to face the hard truths of the city that the others have been oblivious to or just chosen to ignore. His fresh perspective might even provide the Bat-Family with a new way to help their city move forward. As recent events have shown, the old way of doing things hasn't been working for some time now.