In most cases, you don’t need to remove existing insulation, and you’ll be able to apply new insulation while taking advantage of any R-value offered by the previous insulation.
However, there are a few scenarios where this won’t work. If there is a sign of water damage, such as mold, then you’ll want to replace the existing insulation.
You’ll also need to replace the insulation if there isn’t enough room for the R-value you want while keeping the existing insulation in place — such as if you have older insulation with a poor R-value for its density that you’re replacing with a more efficiently insulative material.