You can use a simple block of code either directly from Python window in ArcGIS or as a Python script or as a custom script tool.
Below is a sample code for a script tool. Just add your vector layers into a map document (.mxd) and specify the clip layer and the output geodatabase.
import os, arcpy
arcpy.env.overwriteOutput = True
clip_layer = arcpy.GetParameterAsText(0)
out_gdb = arcpy.GetParameterAsText(1)
mxd_obj = arcpy.mapping.MapDocument("CURRENT")
for lyr in arcpy.mapping.ListLayers(mxd_obj):
arcpy.AddMessage(lyr)
out_layer = os.path.join(out_gdb,lyr.name)
arcpy.Clip_analysis(lyr,clip_layer,out_layer)