Tried a Google Scholar search? https://scholar.google.se/scholar?hl=en&as_sdt=0%2C5&q=tqm+”teacher+education”&btnG= Gives a lot of papers to start with - take help of their list of references to go further. Use then other classic database searches. Search also for literature reviews Directly on this combination or varieties thereof. And try to find a researcher that masters this, and begin communication if possible.
But - are you sure that TQM is so directly applicable or even relevant for teacher education?
I am writing to inform you that I used this literature in my article
Leadership teaching as the most important feature in adult education management.
Please find follows literature:
Ammelburg, G. (1993). Organismus Unternehmen. Düsseldorf: ECON.
Blake, R. R., Mouton, J. S. (1964). The Managerial Grid. Houston: Gulf Publishing Company.
Bolton, R., Bolton, D. G. (2009). People Styles at Work... And Beyond: Making Bad Relationships Good and Good Relationships Better. New York: American Management Association.
Bosworth, K., Pena, T., Judkins, M. (2015) Leadership in American Schools. U: Bosworth, K., (ur.) Prevention Science in School Settings Complex Relationships and Processes (str. 45-66). Springer, New York.
Cass, A. W. (1971). Basic education for adults. A handbook for teachers, teacher trainers, and leaders in adult basic education programs. New York, USA: Association Press.
Drucker, P. F. (2007). MANAGEMENT Tasks, Responsibilities, Practices. New York: TRUMAN TALLEY BOOKS / E.P. DUTTON.
Drucker, P. F. (2011). Managing for the Future. New York: Routledge.
Gay, Sr., P. W., (2008). Leadership core competencies, Strategy Research Project. Carlisle Barracks, U.S. Army War College.
Glasser, W. (1986). Control Theory in the Classroom. New York: Harper Collins.
Gordon T. (2001). Leader Effectiveness Training, L.E.T.: The Proven People Skills for Today’s Leaders. New York: A Perigee Book.
Griffin R. W. (2013). Management (11th ed.). Mason: South-Western.
Knowles, M. S., Holton III, E. F., Swanson R. A. (2005). THE ADULT LEARNER The Definitive Classic in Adult Education and Human Resource Development. San Diego: Elsevier Inc.
Aziz, S., Mahmood, M., & Bano, S. (2018). Total Quality Management: A Frame Work for Higher Education Institution. Journal of Research in Social Sciences, 6(1), 124-141.
Sallis, E. (2014). Total quality management in education. Routledge.
Manivannan, M., & Premila, K. S. (2009). Application of principles of total quality management (TQM) in teacher education institutions. Journal of College Teaching and Learning, 6(6), 77.
Also here in reaserchgate you are able to find some articles
Teacher's quality can be verified through the performance of their students, but to manage teachers quality, they need in service training including workshops, conferences, seminars to upgrade themselves. Teacher qualifications is necessary whenever they need their services, this will help in the process of management.
I am struggling to understand the question - do you mean TQM in respect to the training of school teachers in classrooms? If so, the overarching quality in the UK is initially dictated by the Department for Education but inspection, and adherence to standards, is monitored by Ofsted - the handbook for inspections is here: https://www.gov.uk/government/publications/initial-teacher-education-inspection-handbook and it is through that a judgement on Quality in Teacher Education is derived by the inspectorate for each and every teacher training provider. Hope that helps?