Fiona
I found this link on schools and teachers in Armagh
Those are more commonly used to find the National School attendance registers for pupils and then order and view the registers in PRONI. For the few ones I have consulted in Lurgan and Belfast their teacher was not recorded on the pages. There may be inspectors reports and cash books for some and I see a Lurgan School has "Book entitled School Reports, which gives inspectors' comments on teachers, and overall school performance" but they don't track a teacher's career.
https://www.nidirect.gov.uk/publications/index-school-collectionsTeachers Salary Books PRONI Ref ED/7.
"If you want to find out who taught in particular schools you should consult the Salary books kept by the National Education Board and continued by the Northern Ireland Ministry of Education. The volumes held in PRONI only date from 1899 and are incomplete up to 1905 but thereafter run continuously up to 1927. The pre-1899 volumes and the missing ones between 1899-1905 are in the National Archives of Ireland in Dublin. These salary books will give the names of the teachers, their academic qualifications and their date of appointment and resignation in addition to particulars of their salaries. Salary Books can be found under the PRONI Ref ED/7" They are not online.
https://www.nidirect.gov.uk/publications/national-education-records