the usage of "former"

I met an old teacher of mine the other day

Is fine for talking about any teacher from your infancy to your high school (BrEng secondary) years.

Using former also works well

The other day I met a former teacher of mine, Mr. Smith

If you wanted to specify that this person was the last teacher who ever taught you then I'd go for:

I met Mr. Smith the other day. He was my very last teacher.

A former teacher or previous teacher can be any teacher you have had in the past.

Therefore it does not specifically mean the one you had last, unless it is obvious from the context that they must have been the last teacher you had.

If you need a synonym for last teacher, then most recent teacher does the job.