So I recently changed my job, and have been given a req for a new hire reporting to me. I may be able to announce the position on Linked In. For ethical reasons, I will NOT be approaching anyone at my former company about this, but what if someone from that company approaches me after seeing it on Linked In? Would it be ethical to allow them to apply for the job?
Ethics when former colleague applies for position
There is nothing unethical about hiring former colleagues, or even headhunting so long as there are no constraints from your agreements with your former workplace.
The ethical thing to do if there is any doubt in your mind is just to stay out of it.
Unless you're the hiring manager or have been tasked to do that role, you have no reason to and it's unprofessional to preempt someone else's role. Companies hiring people are usually professionals in their own right. They may have policies on hiring practices, advertising positions and everything else. Just as any other role may have policies.
There is no ethical dilemma interviewing, I have blocked people from getting jobs because I personally knew them to be useless, so interviewing a former colleague does sometimes give you more insight. But I wouldn't block them just because I used to work with them. It's actually more of an ethical issue if you bring in candidates for an interview because that means you will probably favour them over other candidates that came in on their own or by other means.
I guess it depends on the culture, but I'd have no qualms about not only letting developers from my old company apply.
Hell, absent other restrictions (NDA/non-compete/non-solicitation in contract), I often reached out to talented colleagues that I've worked with previously to encourage them to apply for the same company I worked for, when I found the company paying, and treating the employees well.
Did you sign a non-solicit agreement with your previous company?
My assumption is that this is why you are asking this question. If you did, then check the terms of it. If you agreed not to hire away any of your previous co-workers for a specific period of time, then you're bound by that, depending on the parameters.
Otherwise, you might need to edit this question to be more clear about what you're asking. There is no ethics-based reason to not allow your previous co-workers to apply.