It might be a bit verbose, but the obvious answer would be:
SELECT * FROM tblDBS_Details
WHERE
CASE @ExpiryType
WHEN 0 THEN DATEADD(D, @ExpiryValue, @DateOfIssue)
WHEN 1 THEN DATEADD(W, @ExpiryValue, @DateOfIssue)
WHEN 2 THEN DATEADD(M, @ExpiryValue, @DateOfIssue)
WHEN 3 THEN DATEADD(Y, @ExpiryValue, @DateOfIssue)
END <= GETDATE()