How to remove unnecessary symbol in the column in SQL Server 2008
If it is just one symbol for each value returned, then you could do this

It seems like you have some trailing spaces, that is why RTRIM is used, or DATALENGTH() if they need to be preserved. Thanks to   @Denis Rubashkin for pointing that out.

Solution where the spaces are removed 

SELECT DISTINCT RIGHT(RTRIM(NEW),(LEN(RTRIM(NEW)) - 1))
FROM [FixedAsset Control].[dbo].[NewViewReport]; -- RTRIM takes care of the trailing spaces


Solution without removing the spaces:

SELECT DISTINCT RIGHT(NEW,((DATALENGTH(NEW) / 2) - 1))
FROM [FixedAsset Control].[dbo].[NewViewReport]; -- Datalength also counts spaces


And if you want to update the column after you validated that the result is correct:

UPDATE[FixedAsset Control].[dbo].[NewViewReport]
SET NEW = RIGHT(RTRIM(NEW),(LEN(RTRIM(NEW)) - 1));


Or

UPDATE[FixedAsset Control].[dbo].[NewViewReport]
SET NEW = RIGHT(NEW,((DATALENGTH(NEW) / 2) - 1));


Testing

CREATE DATABASE [FixedAsset Control]
USE [FixedAsset Control]
GO
CREATE TABLE  [dbo].[NewViewReport] ([NEW] nvarchar(255));

INSERT INTO [dbo].[NewViewReport]([NEW])
VALUES('·OUTGOING QC OFFICE');

SELECT DISTINCT RIGHT(RTRIM(NEW),(LEN(RTRIM(NEW)) - 1))
FROM [FixedAsset Control].[dbo].[NewViewReport];


Result

(No column name)
OUTGOING QC OFFICE