When I was in flight training, I was debriefing when someone came into the office doing just that. The owner was in the office at the time, and the dialogue went something like this:
job seeker: Hey, how are you doing, do you have a moment?
owner: Sure, what's up? js
: I just got me CFI, and ...
ow: Congrats!!! js
: Thanks! I was wondering if you guys could possible use a motivated flight instructor full or parttime, or have other related openings like ground instructor or something.
ow: Right now we don't, but why don't you leave your contact details? js
: Sounds fair, here is a copy of my CV and contact details. Thanks for your time!
ow: No worries, you're welcome.
About three months later, we had a new parttime CFI on the roster.