The phrase "teaching gig" typically refers to a temporary or part-time job as a teacher, usually in the context of working on a short-term or casual basis, rather than a permanent or full-time position. Full definition
Part of your final conversation around starting a new teaching gig should include, in writing, how you will be paid and if you need to fill out any paperwork. (mindbodygreen.com)
In fact, most women keep the whole thing quiet and, at most, discuss it with one girlfriend who is doing the same thing and maybe taught them the gig. (businessinsider.com)
To land a two year teaching gig they go to Happy Hour. (nancyebailey.com)