We use publicly available, longitudinal data from Washington state to study the extent to which three interrelated processes--teacher attrition from the state teaching workforce, teacher mobility between teaching positions, and teacher hiring for open positions--contribute to "teacher quality gaps" (TQGs) between students of color and other students in K-12 public schools. Specifically, we develop and implement an agent-based model simulation of decisions about attrition, mobility, and hiring to assess the extent to which each process contributes to observed TQGs. We find that eliminating inequities in teacher mobility and hiring across different schools would close TQGs within 5 years, while just eliminating inequities in teacher hiring would close gaps within 10 years. On the other hand, eliminating inequities in teacher attrition without addressing mobility and hiring does little to close gaps.