ORA-04082: NEW or OLD references not allowed in table level triggers

CREATE OR REPLACE TRIGGER my_test_trigger
BEFORE INSERT ON my_table
DECLARE
   v_out   number ;
BEGIN
   my_procedure(:new.column1, :new.column2, v_out) ;
   :new.column3 := v_out ;
END;

There are two types of DML triggers: statement level and row level. The statement level trigger fires once per transaction, while the row level trigger fires for each record effected, per transactions. In order to use :new or :old, the trigger must be a row level trigger. The trigger you have created is a statement trigger. To change your trigger to a row level trigger, you must add the following line:

        FOR EACH ROW

Your trigger will then look like:

CREATE OR REPLACE TRIGGER my_test_trigger
BEFORE INSERT ON my_table
FOR EACH ROW
DECLARE
   v_out   number ;
BEGIN
   my_procedure(:new.column1, :new.column2, v_out) ;
   :new.column3 := v_out ;
END;