It sounds like you are trying to create a new category based on the PayCode values. You can try something like this:
SELECT CASE
WHEN Pay_Code = 'OT' THEN 'OT'
WHEN Pay_Code IN ('VACP','PERS') THEN 'Paid Shrink'
WHEN Pay_Code = 'REG' THEN 'REG'
WHEN Pay_Code IN ('VTO','LOA','BER') THEN 'Unpaid Shrink'
ELSE 'Unknown'
END as PayCode_2
,YEAR(Date), WEEK(Date,4), SUM(Hours), Site, Pay_Code
FROM table
GROUP BY PayCode_2, Pay_Code, Site, YEAR(Date), WEEK(Date,4)