The phrase "of the teaching profession" refers to things or people that are associated with or connected to the job of being a teacher. Full definition
We decided to take advantage of the depth and duration of these data to explore our questions about the demographic status of the teaching profession. (ascd.org)
So how in the world can I be so optimistic about the future of the teaching profession? (kappanonline.org)
He continued, stating the profession is attracting the country's top graduates, that he believed the prestige of the teaching profession is on the increase. (educationbusinessuk.net)