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create table Test_Table (
EID int,
Hold varchar(20),
Source varchar(50)
);

insert into Test_Table values
(3232 , 'KLME', 'jame.k@gmail.com'),
(null , 'KLME', 'https://google.com'),
(null , 'EEME', 'david.e@gmail.com'),
(null , 'JJIN', 'Test@gmail.com'),
(7232 , 'JJIN' , 'https://google.com');
5 rows affected
select t.Hold, s.Eid
from Test_Table t
inner join (
select Hold, max(EID) as Eid
from Test_Table
group by Hold
) s on s.Hold = t.Hold
Hold Eid
EEME null
JJIN 7232
JJIN 7232
KLME 3232
KLME 3232
Warning: Null value is eliminated by an aggregate or other SET operation.

Update t
SET Eid = S.Eid
FROM Test_Table t
inner join (
select Hold, max(EID) as Eid
from Test_Table
group by Hold
) s on s.Hold = t.Hold
Warning: Null value is eliminated by an aggregate or other SET operation.
5 rows affected
SELECT *
from Test_Table
EID Hold Source
3232 KLME jame.k@gmail.com
3232 KLME https://google.com
null EEME david.e@gmail.com
7232 JJIN Test@gmail.com
7232 JJIN https://google.com