Nothing much! The airport checks every complaint using its own internal protocol to assess risk. - not noise. In other words, it checks to see if the aircraft was flying safely or not, if it was where it was supposed to be at a correct altitude. And that's it. 

It then emails you to tell you that the aircraft was fine. There is never any attempt to address the noise issue by undertaking to make changes. 

“The main purpose of investigating a complaint at NIAL is to determine whether the corresponding aircraft movement(s) are compliant with CAA procedures or not. A complaint can’t be resolved if it isn’t breaching any operational regulations.”
(This from the airport's Noise Action Plan 2025 consultation responses, page 76)