I was wondering if anyone had any tips about reaching out to HR reps on behalf of others?

It kind of depends and keeping your response in mind. It really depends on your approach and what you are calling them on behalf of others for. As for an initial thing when I was in and am out now and doing admin stuff if I call somebody on behalf of the person I'm working for I say hello this is John Doe calling on behalf of Jane Doe. I'm calling because ... or you could say something along the lines of you are calling representing whoever to get them an interview for whichever position they have and then pick a couple main strong points that will stand out.