To solve your problem as described in your question, consider the following:
DECLARE @NewQNo VARCHAR(20)
DECLARE @OriginalQNo VARCHAR(20)
SET @OriginalQNo = 'res/12-19/001'
SET @NewQNo = RIGHT('00' + CAST(RIGHT(@OriginalQNo, 3) + 1 AS VARCHAR), 3)
SET @NewQNo = LEFT(@OriginalQNo, LEN(@OriginalQNo) - 3) + @NewQNo
PRINT @NewQNo
In order to format the number as a 3-digit one with trailing zeroes, you simply prepend two zeros as a string to the start of the number and then extract the right-most three digits, which will produce in this case 002.
In order to also include the rest of the question syntax, the second SET line prepends the starting characters of the question (in this case, res/12-19/ to the completed 3-digit string.
Output:
res/12-19/002