asongoftheories answered:

nobodysuspectsthebutterfly:

Oh, I’m sure Arya’s role in Braavos is going to be important. Certainly more than just the Faceless Men… especially because I’m sure she won’t stay with them forever, as her hiding of Needle — her “true self” — suggests. I mean, I’ve said before that Arya’s plot could go anywhere, and that includes within Braavos as well as outside of it.

And yes, Braavos is very well established within the plot, far more than the other Free Cities, at least until ADWD gave us so many details about Volantis. Which is probably because the cities as foils to each other, Volantis as the claimed heir of Valyria and Braavos as the bastard child who ran away and hid. (The fact that Braavos is anti-slavery and Volantis may be facing a slave rebellion soon is another way they might be at odds.)

Back to Arya and the Iron Bank plot: she definitely could find out about Jon Snow’s debt. Possibly she might somehow encounter Stannis’s emissary, Justin Massey, when he’s hiring sellswords. (And will Tycho Nestoris and Massey bring certain unpleasant news from the Wall as well? Anyone’s guess right now.)

But if I had to bet how Arya would get involved with Iron Bank storylines… well, in ADWD’s epilogue, we learned Ronnet Connington brought the remainder of Gregor’s men to King’s Landing. (Possibly including Dunsen and Raff the Sweetling, unless they were the ones Randyll Tarly gelded/hanged.) Kevan Lannister told Harys Swyft that since he feared assassins, he should hire them as guards. And he also commanded Swyft to go to Braavos and deal with the Iron Bank.

So, assuming that Kevan’s assassination isn’t changing any of those plans (and actually it almost makes it a certainty that Swyft will hire guards)… that could be two of the five remaining names on Arya’s kill list, heading to Braavos where Arya is. If she encounters them, the repercussions (whatever they may be, whatever she chooses to do) could certainly have an effect on the Iron Bank plotline… and her.

But truly, Arya’s storyline could go anywhere. All we know is that she’s to go to Izembaro to begin her apprenticeship, and that could be a person — a Faceless Man or someone who works for them — or a place, or who knows. All kinds of possibilities and potential for her, really.

(I very much doubt she’ll take the role of a courtesan, though. Arya is still just 11 and has not yet hit puberty, and so far we’ve just seen the Faceless Men change her face, not her body. (I don’t think we’ve seen FM change bodies at all, for that matter, so who knows if they even can?) Unless GRRM wants to echo a certain unpleasant plot point of V for Vendetta, I imagine he’d avoid that kind of “seduction” role for Arya for now.)