You should clean the handle with vinegar and water to see if it's clogged. If this doesn't work, you'll need to replace the handle or the plunger. Make sure the handle is connected to the rod. If it's not, then you'll need to replace the rod.
Having a broken toilet handle is frustrating, and it’s not always super easy to find the right part for the toilet. Some are universal and some are specific to the toilet model. So, the best way to ensure you’re getting the right part is to call in a plumber.