Surely they’re gonna have a story that shows how Ariel’s mother died, (they love killing off parents on this show). In Disney she was crushed by a pirate ship, but they could do anything with it. Make her go steal ink from a Kraken and that sets up a dangerous situation for her. Make her seriously injured in the attempt, and you’ve got a situation where Triton would be desperate enough to give up his trident if Rumple had a way to heal her, (which ultimately didn’t work, and she died). That would connect the story of what happened to Ariel’s mother to something we’ve already seen specifically mentioned, and would set up Ariel having animosity towards Rumple in present day. Would tie it all together nicely.
They could just do a lot of exposition as well; they could do a lot of things for Ariel through dialogue, actually. It depends on if she’s going to be integrated into the cast. If she’s a one time character and maybe only appears in one or two episodes, then all they have to do is give a little bit of background but nothing more. Like Robin Hood; his story was really only there to highlight Rumbelle (unless he really is Tamara’s father).