You would need to use two parameters for te position number, the old one and the new one. COnsider the following:
Create procedure [dbo].[Update_Position]
(@Position_Number_old char(15),
@Position_Number_new char(15),
@Grade varchar(5),
@StartDate varchar(1000)
)
as
update PositionInformation
set Position_Number=@Position_Number_new,
Grade = @Grade,
StartDate =@StartDate
where Position_Number=@Position_Number_old
But before jumping to that, in my opinion, you should really modify the parameter types and column types correspondingly. Never store dates or number in character types. Instead use proper types such as date, int, float .