So, I've been thinking that Gates if going to turn out to be helpful - in the long run - for Beckett. I also think it would be cool if she's the one who brings Kate back in. She was very shocked that Kate resigned. I do think there's gonna be some friction though. We don't know if Ryan told Gates about Captain Montgomery's involvement in the situation or not. In either case she's going to have to find out. She's not going to care about dragging his name through the mud in order to get this guy. She also will probably partially see it as a career maker to bring this guy down. However, unlike Beckett, Gates believes very strongly in teamwork. She's gonna what the best people on this. She's also worked IA though and hates Dirty Cops.
So why would Gates bring her back in? Because I think Gates believes BECKETT is a good cop. Remember, she warned Beckett about Castle becoming a distraction to her work. In her own way, the few times it's been just Gates and Beckett, Gates has basically tried to mentor her. With the dirty cop angle Gates may find that having the best work on this has to mean Beckett because Gates doesn't know who else is dirty, plus it's safer for both Kate and Gates to have Kate on duty and Gates knowing what she's doing.
I think Gates' past is what drove her to IA, and that when she finds out about Beckett's shooting being connected to her mom's murder and her mom's murder is connected to dirty cops, Gates will have a better understanding of WHY Beckett went out on her own, even though she won't condone it.