It could go up, down, or remain the same. Standard deviation is a measure of how "spread out" the values are, independent of how many there are (that's why you divide by n-1). Let's say I have these test scores for three people:
70 80 90
The standard deviation of these three scores is 10. Now I add two more test scores:
70 75 80 85 90
The standard deviation goes down to 7.91. If I added two different scores:
60 70 80 90 100
the standard deviation would go up to 15.81, because the scores are definitely more spread out.