Group by in subquery and base query sql server

No, you will not be able to do that as the SUB QUERY in the SELECT list will then return more that 1 Value.

You need to do it in a SUB Query in the FROM clause

Something like

 SELECT Day, 
        SUM(Regular + Extra + Overtime) AS [Potential Hours],
        SubSum AS [Billed Hours]
FROM    Billable AS Billable1 LEFT JOIN
        (
            SELECT  Day,
                    SUM(Extra + Regular + Overtime) AS SubSum
            FROM    dbo.TICPlus_Effort_Billable_Only
            WHERE   (Manager NOT LIKE '%manager1%')
            GROUP BY Day
        ) s ON  Billable1.Day = s.Day
GROUP BY    Day