This plugin will delete all fields/columns from a vector layer which has all values equal to NULL.
https://plugins.qgis.org/plugins/delete_null_fields
Basically this plugin has one input which is Vector Layer in QGIS or you can give path to local vector data, after choosing one layer from dropdown, it will list all the fields which has all of its values equal to NULL or Empty. Then you can select fields that you want to delete from that particular file. Now it depends on your choice if you want to create temporary layer or want to export the updated temporary layer into shapefile, if you want to create temporary layer left the Output field empty or give export path with filename+extension which is shapefile(.shp).