Kulitja has held an important position within her community for several years. She has been a member of both the Muṯitjulu Community Council and the Board of Management of Uluṟu-Kata Tjuṯa National Park. In 2006, she became the chairperson of Maṟuku Arts. In October 2007, she was elected for a two-year term as a director on the Ngaanyatjarra, Pitjantjatjara and Yankunytjatjara (NPY) Women's Council.