Q:

Student:Classmate::Teacher:____________?

A student is a classmate, schoolmate, etc. to another student. But what is a teacher to another teacher? 
Couldn't it be colleague? Surely not, because a colleague could be any employee working with another.

A:

The generally used word is in fact colleague. You may also hear phrases like 'fellow faculty member' or 'fellow teacher' or 'coworker'.
There is no specific variant of the word for educators.

A:

You are right that classmate is more specific than colleague, and that more context can be inferred from the word classmate than from the word colleague. But I don't think the implied assertion – that there must be a similarly-specific word for teachers – is correct.  
Similarly, I think you might have a hard time finding a specialized word for "fellow custodian" or "fellow cafeteria worker" or "fellow guidance counselor" or "fellow bus driver."  Not every group at the school will have a word that says, essentially, "one of us."
I thought of one candidate word – faculty – but I don't think that's a precise fit.  A school might have a faculty lounge and a student lounge, but it would not have a classmate lounge.  In the student lounge, a student might run into a classmate, but, in the faculty lounge, a teacher would run into a... ?
Colleague; that's what I'd say.

