If you want to find people in a certain academy, you can just use the search function?

The idea is, I don't know what academy people who moved away train at now, or what the home academies of the other people in the university club are. So if they could list that they used to train at my home academy, or they train at the university club in addition to their home club it makes them easier to find.

Perhaps the "Location" field on past belt promotions could be searchable? (If you've earned the previous ranks elsewhere and have since relocated, one could find people who have once been at a certain academy... I think this was your point?) Albeit people tend to put random stuff on that field & not strictly gym and city names.

Promotion location would catch some cases. Maybe what I'm thinking of isn't as common as it seems to me. Another example, my gym has guys whose jobs bring them to town for just a couple of months out of the year, they'd probably list some other gym on their profile under academy, and will get their promotions from that academy, but they also actively train at our gym for some portion of the year.