As @champezius mentiond@user2856 mentioned, the Erase‘Tabulate Intersection’ tool would be the easiest way. Also, as @champezius mentiond, the Erase tool could also be helpful. However, that requiresthese tools both require an advanced license, which is rather costly.
If you don't have an advanced license, then you could use the Union tool for this, and then delete the polygons that have an FID_clipping_feature_class <> -1. What ever is left would be the area that you're interested in.
(The Union tool also adds all attributes from both of the input feature classes to the output feature class.)
See Union tool documentation for details: https://pro.arcgis.com/en/pro-app/latest/tool-reference/analysis/union.htm
To actually calculate the percentage, you would have to join your original feature class to the union-output feature class based on the FID (ObjectID) of the original feature class and the FID_input_feature_class of the union-output feature class. Then use the area attribute of both to calculate the difference, or percentage.