Once you become an Indiana resident, you'll need the Indiana license (i.e. your NY license would cease to be valid here).
I don't know that having a current NY carry license figures into the application calculus at all.
It would be nice to see some future legislation cover this gap by making the state license of a new resident valid for 90 days, or if the IN LTCH has been applied for then valid until that's approved/disapproved, or something similar.
Good place to start - https://www.in.gov/isp/firearms.htm
I will be moving to Aurora In. in July. I want to get my carry permit. Will Having one From New York State help or hinder?
Just because no one else has said it, Indiana doesn't have a "carry permit". We have a License To Carry Handgun AKA a LTCH or Larry. And there is no requirement to conceal. Open, concealed, or duct tapped to your forehead it doesn't matter.
And welcome to Indiana and INGO.