SET NOCOUNT ON;
USE tempdb;
IF OBJECT_ID('dbo.t') IS NOT NULL
BEGIN
    DROP TRIGGER t_trig;
    DROP TABLE dbo.t;
END
GO
CREATE TABLE dbo.t
(
    ID INT NOT NULL
    , ID2 INT NULL
);
GO
CREATE TRIGGER t_trig ON dbo.t
WITH EXECUTE AS OWNER
AFTER INSERT
AS
BEGIN
    UPDATE dbo.t
    SET ID2 = ID
    WHERE EXISTS (SELECT 1 FROM inserted i WHERE i.ID = dbo.t.ID);
END
GO
CREATE LOGIN tLogin WITH PASSWORD = 'QWERFsdf23454%';
CREATE USER tLogin FROM LOGIN tLogin WITH DEFAULT_SCHEMA = dbo;
GRANT INSERT ON dbo.t TO tLogin;
DENY UPDATE ON dbo.t TO tLogin;

EXECUTE AS USER = 'tLogin';
SELECT SUSER_SNAME();
INSERT INTO dbo.t(ID) VALUES (1);
REVERT

SELECT *
FROM dbo.t;

DROP USER tLogin;
DROP LOGIN tLogin;