Most of the religious orders that have priests are involved in education either as the bulk of their ministry or as one part. The only caution is to inquire into how orthodox are the education ministries where they are presently working. Check out the website of the Cardinal Newman Society. It not only describes many colleges and some high schools where religious orders are, they also give some measurable criteria to look for. Just finding out how common the Sacrament of Confession is will tell you more than thick manuals by the PR department.
I don’t much care if the religious orders boast of many centuries of saints and Catholic heritage (i. e. the past). Many religious priests now are stuck in situations that are very far removed from the Catholic heritage, though institutions still brag about it in recruitment of students, and seminarians. On the other hand, many religious orders founded in the last 40 years are totally immersed in Catholic faith in education **in the present. **
My suggestion is to find high schools, colleges, catechetical centers or Newman Centers that are solidly faithful to Catholic doctrine and practice B]in the present. Then find out which religious orders are working there. There may be a state university that is hostile to Christianity, but a religious order sponsors an excellent campus ministry parish. Or there could be another kind of ministry through communications media, adult education, or other in which you can use your education training.