Pass in the year as a parameter:
DECLARE @YEAR VARCHAR(4)
SET @YEAR = DATEPART(YEAR,GETDATE())
SELECT
case
when Convert(varchar(8), getDate(),1) between '01/01/'+ @YEAR and '03/31/'+ @YEAR then '04/01/'+@YEAR+' - 06/30/'+@YEAR
when Convert(varchar(8), getDate(),1) between '04/01/'+ @YEAR and '06/30/'+ @YEAR then '07/01/'+@YEAR+' - 09/30/'+@YEAR
when Convert(varchar(8), getDate(),1) between '07/01/'+ @YEAR and '09/30/'+ @YEAR then '10/01/'+@YEAR+' - 12/31/'+@YEAR
when Convert(varchar(8), getDate(),1) between '10/01/'+ @YEAR and '12/31/'+ @YEAR then '01/01/'+@YEAR+' - 03/31/'+@YEAR
end