Wallace was elected the Chief of the Eastern Shawnee Tribe of Oklahoma in 2006. She was the first woman ever elected to this office. Chief Glenna was employed at Crowder College for over 38 years in various capacities from Interim Academic Dean to Title III Director.

The Eastern Shawnee Tribe of Oklahoma is one of three federally-recognized Shawnee tribes. In the 1870s Eastern Shawnee tribal membership dropped to 69. In 2010, the Eastern Shawnee tribe had almost 2800 tribal citizens, own approximately 1,000 acres, employ over 600 in several businesses and continue to embark upon new ventures.