(a) you don't need reference from a partner. Getting reference from a more junior person is as powerful to land you the interview as that from a Partner. And beyond that, both are worthless.
(b) to get references in general, impress people. There is no way to force it, but networking with a handful of people in a targeted way (don't blast the office with requests for coffee chats on Linkedin - they'll know that you're wasting their time). Tell your story and impress them with your wits, ambition and humbleness. In order for them to recommend you, they'll need to trust you, so of course it's always best to build on commonalities: start with friends and acquaintance, then alumn from the same school or club, then strangers.
Not much more you can do - as I said: you can't force it.