You can not have a COMMIT inside a trigger. Your UPDATE will be committed as soon as the INSERT to the table1 is committed.
But to achieve what you want you can use an autonomous transaction. For example,
CREATE OR REPLACE TRIGGER mytrg
AFTER INSERT ON table1 FOR EACH ROW
DECLARE
PRAGMA AUTONOMOUS_TRANSACTION;
BEGIN
myschema.myproc(:new.ID, :new.NAME, :new.TYPE_CODE, :new.LANGUAGE);
COMMIT;
END;