Syntax error with NEW while creating a trigger in PostgreSQL

You should read more about trigger procedures in official docs. When you call trigger function OLD, NEW and bunch of other things or passed implicitly through TG_NARGS and TG_ARGV, so you shouldn't do it by yourself.

CREATE OR REPLACE FUNCTION INVENTORY_ENTRY_NEW_PRODUCT()
RETURNS TRIGGER AS $INVENTORY_ENTRY_NEW_PRODUCT_TRIGGER$
BEGIN
  -- Here you can access NEW.productcode

RETURN NULL;
END;
 $INVENTORY_ENTRY_NEW_PRODUCT_TRIGGER$ LANGUAGE plpgsql;


CREATE TRIGGER PRODUCT_ADD_TRIGGER AFTER INSERT
ON product FOR EACH ROW
EXECUTE PROCEDURE INVENTORY_ENTRY_NEW_PRODUCT();

UPDATE

So in your case trigger should look like above and trigger function like below:

CREATE OR REPLACE FUNCTION "INVENTORY_ENTRY_NEW_PRODUCT"()
  RETURNS record AS
$BODY$
-- Declare the required variables.
DECLARE
    -- Inventory row that stores the result of the query on the inventory table.
    inventoryrow inventory%ROWTYPE;
    result record;
BEGIN

    SELECT * INTO inventoryrow from inventory where fk_productcode = NEW.productcode;

    IF NOT FOUND THEN
        -- INVENTORY TRANSACTION CAN BE ADDED.
        -- An inventory transaction can be added to the inventorytxns table
        INSERT INTO inventorytxns (fk_productcode,fk_txntypeid) VALUES(NEW.productcode,6);

        -- Once a row is added into the inventory txns table, it automatically adds data into the inventory table.
        SELECT * INTO result FROM INVENTORY WHERE fk_productcode = NEW.productcode;

        IF NOT FOUND THEN
            -- RAISE AN EXCEPTION. THIS OPERATION IS SUPPOSED TO HAPPEN.
            RAISE EXCEPTION 'Product with product code % added in inventorytxns table but not added in inventory table',NEW.productcode;
        END IF;
        -- Transaction type 6 represents addition of a new product transaction type.
    END IF;

    RAISE DEBUG 'Product with product code % already available in inventory',productcode;

END;
-- Check if the inventory entry already exits in the inventory table.
$BODY$
  LANGUAGE plpgsql VOLATILE
  COST 100;

From docs

When a PL/pgSQL function is called as a trigger, several special variables are created automatically in the top-level block. They are:

NEW

Data type RECORD; variable holding the new database row for INSERT/UPDATE operations in row-level triggers. This variable is NULL in statement-level triggers and for DELETE operations.

OLD

Data type RECORD; variable holding the old database row for UPDATE/DELETE operations in row-level triggers. This variable is NULL in statement-level triggers and for INSERT operations.

...

Summary

You should remember that trigger functions are really different from 'normal' PostgreSQL function and it can be called only by trigger, which provides proper context. For the other hand NEW. OLD. and other trigger related stuff is completely meaningless outside trigger execution context.