Automatic insertion of calculated values to another
I've reduced your table schema in this way:

CREATE TABLE AddItems
(
Item_ID int IDENTITY PRIMARY KEY,
Quantity int NOT NULL,
Item_Code varchar(10) NOT NULL,
Item_Description varchar(100) NOT NULL
);

CREATE TABLE Products
(
Product_Id int IDENTITY PRIMARY KEY,
Item_Code varchar(10) NOT NULL,
Item_Description varchar(100) NOT NULL,
Available_Quantity int NOT NULL DEFAULT(0)
);


You can add a trigger like next one:

CREATE TRIGGER trg_AddItems_Insert
ON AddItems
FOR INSERT
AS
BEGIN

    /* update existing products */
    UPDATE   p
    SET      Available_Quantity = Available_Quantity + Qty
    FROM     Products p
    JOIN     (SELECT   Item_code, SUM(Quantity) Qty
              FROM     inserted
              GROUP BY Item_Code) s
    ON       p.Item_Code = s.Item_Code;


    /* insert new products */
    INSERT INTO Products
    (Item_Code, Item_Description, Available_Quantity)
    SELECT   i.Item_Code, i.Item_Description, Sum(Quantity)
    FROM     inserted i
    WHERE NOT EXISTS(SELECT 1 
                     FROM Products 
                     WHERE Item_Code = i.Item_Code)
    GROUP BY i.Item_Code, i.Item_Description;

END
GO


This solution assumes AddItems table won't be modified or deleted, it is only used to add new rows. If some user can UPDATE or DELETE rows, you should consider either:


Add one trigger for DELETE and another for UPDATE.
Use stored procedures to INSERT/UPDATE/DELETE rows.


Now, let me insert some values:

INSERT INTO AddItems VALUES 
(10, 'AAA', 'PRODUCT A'),
(5,  'AAA', 'PRODUCT A'),
(7,  'CCC', 'PRODUCT C'),
(1,  'BBB', 'PRODUCT B');

INSERT INTO AddItems VALUES 
(25, 'AAA', 'PRODUCT A'),
(10, 'BBB', 'PRODUCT B'),
(3,  'CCC', 'PRODUCT C'),
(5,  'CCC', 'PRODUCT C');


And this is the final result:




SELECT * FROM PRODUCTS;
GO



Product_Id | Item_Code | Item_Description | Available_Quantity
---------: | :-------- | :--------------- | -----------------:
         1 | AAA       | PRODUCT A        |                 40
         2 | BBB       | PRODUCT B        |                 11
         3 | CCC       | PRODUCT C        |                 15



db&lt;>fiddle here