Conversion of Row into Column
Use a split string table valued function and CROSS APPLY.

--sample split string TVF
create FUNCTION [dbo].[SplitString]
(    
      @Input NVARCHAR(MAX),
      @Character CHAR(1)
)
RETURNS @Output TABLE (
      Item NVARCHAR(1000)
)
AS
BEGIN
      DECLARE @StartIndex INT, @EndIndex INT

      SET @StartIndex = 1
      IF SUBSTRING(@Input, LEN(@Input) - 1, LEN(@Input)) &lt;&gt; @Character
      BEGIN
            SET @Input = @Input + @Character
      END

      WHILE CHARINDEX(@Character, @Input) &gt; 0
      BEGIN
            SET @EndIndex = CHARINDEX(@Character, @Input)

            INSERT INTO @Output(Item)
            SELECT SUBSTRING(@Input, @StartIndex, @EndIndex - 1)

            SET @Input = SUBSTRING(@Input, @EndIndex + 1, LEN(@Input))
      END

      RETURN
END
GO




--demo setup
Declare @Table1 table (HIC_Number varchar(5), DateFrom date, DateTo date, PrimaryDx varchar(5), AdmitDX varchar(5), AdditionalDx varchar(100))
insert into @Table1 (HIC_Number,DateFrom,DateTo,PrimaryDx,AdmitDX,AdditionalDx) values
('A','1/1/2018','1/25/2018','E559','E459',';E559;E099;E1121;E784;E039;J449')

--the solution
SELECT HIC_Number
    ,DateFrom
    ,DateTo
    ,PrimaryDx
    ,AdmitDX
    ,Item
FROM @table1 a
CROSS APPLY dbo.SplitString(a.AdditionalDx, ';')
WHERE item &lt;&gt; ' '




| HIC_Number | DateFrom   | DateTo     | PrimaryDx | AdmitDX | Item  |
|------------|------------|------------|-----------|---------|-------|
| A          | 2018-01-01 | 2018-01-25 | E559      | E459    | E559  |
| A          | 2018-01-01 | 2018-01-25 | E559      | E459    | E099  |
| A          | 2018-01-01 | 2018-01-25 | E559      | E459    | E1121 |
| A          | 2018-01-01 | 2018-01-25 | E559      | E459    | E784  |
| A          | 2018-01-01 | 2018-01-25 | E559      | E459    | E039  |
| A          | 2018-01-01 | 2018-01-25 | E559      | E459    | J449  |