Perhaps I skimmed it over, but I don't think there's anything in the comic books or LoK which really describes what Katara's role was after she got married. I know for the other members of the Avatar team, their roles were explicitly stated. Zuko obviously ruled over the Fire Nation, Sokka was a representative in Republic City and later chief of the Southern Water Tribe, Toph was Chief of Police, etc.
I know that Katara in LoK now lives in the Southern Water Tribe teaching bending, her culture, and being a healing master. However, for most of her life, she must have lived in Republic City with Aang and her kids. Did she adopt a traditional motherhood role where she focused on developing cultural and ethical values in her children, much like those that we see in her? This might just be the case. Just as Katara and Sokka meant everything for Kyi (more than her own life), perhaps Katara feels the same for her children.
That's my guess, but I could be wrong. Did she also have another more professional role that I have overlooked?