Roughly, there are two ways I do UX research:
In most cases this means I have to dive into the tools available to gather as much data as possible about this thing turning up. In general the starting point here is Google Analytics to find out which data is available. (It's convenient here that I was responsible for the implementation of Google Analytics, Universal Analytics and the Google Tag Manager the last few years at debijenkorf.nl. That helps in knowing what data is available and what the possibilities are.)
This means checking the available tools regularly, preferably on a daily basis (in my experience doing this daily will give a 'feel' - a pulse if you will - of the product; which also means you will quickly pick up 'anomalies', that may indicate user-problems). This is also were JIRA comes into the picture: I use it to create files around returning issues. Gathering as much 'proof' for an issue as possible (collecting excels, screenshots, feedback, inspiration from competitors/ peers, etc.).
In both cases, at some point, a product owner decides this user-issue or business-need needs to be addressed and a design is needed. And that's when the cycle starts as described in the UX design process.
As you can see, research can not live without design. And vice versa.