Sansa is the Lady of Winterfell. Arya is her Sword.
The old Stark saying of “He who passed the sentence should swing the sword” is totally reinterpreted here. Neither Sansa nor Arya would have the physical ability to wield Ice, their ancestral greatsword, if the blade was still there. So, instead, they became to the two halves of that whole statement.
Arya acknowledges that she could never be the Lady of Winterfell, not like Sansa could, so she became something else. Sansa couldn’t kill someone, not like Arya or her brothers or her father could, but she doesn’t need to do that. What I think we’ll see in the final season of Game of Thrones is Arya operating as the metaphorical sword that Sansa wields in the defense of their home.
After all, Sansa and Arya are opposite sides of the same coin. Sansa can rule and protect the North as the Lady of Winterfell and Warden of the North. Arya can serve as the Sword of Winterfell, keeping the peace, executing those who commit treason, and defending their home in the ways she was trained.