The suggestion by Leo will work, but you will need to deal with the locks that are placed on a file geodatabase by ArcGIS Server.
I would suggest instead using the DeleteFeatures_management tool followed by the Append_management tool to avoid the locks.
You would have to stop the affected service of the file geodatabase if you want to delete the feature class and create it brand new each week. Then you would have to restart the service once the feature class creation has been completed.