Dating former student? Here's the situation: She was an undergrad, I was a grad TA. At that point, our interactions were totally professional and limited to the classroom.  However, she and I both since graduated and left the college/city where we got our degree.  I now am at another university working as a postdoc and she is working outside of academia.  We ran into one another and started spending time with one another.  Our relationship has been platonic, but I get the sense that it could go further, which I wouldn't necessarily be opposed to. I can't imagine that there would be legal problems with pursuing a romantic relationship, but would there be ethical or professional concerns (as an early career academic)?
There are professional/ethical rules at many universities relating to dating between students and staff, but these do not extend to imposing a permanent moratorium on dating between people who have previously attended that institution.  Essentially you are asking if there are any professional or ethical issues in dating another adult who has no connection whatsoever to your current employer.  I cannot see any issue.