To add an attribute to a block that’s already defined (and used) in the drawing, simply issue the BEDIT command, select the block defined and use the ATTDEF command. It’s likely you will want to turn on the “Align below previous attribute definition” toggle. Then close the Block Editor and Save Changes.
The most important consideration now is that existing inserts don’t have a placeholder for your new attribute! AutoCAD’s built in ATTSYNC command can correct this. Issue the command, press enter to <Select> and pick any insert of your block, press enter to confirm. All the instances of your insert now display the newly added attribute with the default value. You can now simply double-click an insert to change the value in the enhanced attribute editor.