Authors use many techniques to create suspense, but one of the most common is the use of setting. To answer this question, you need to ask yourself " what is it about this story's opening that makes me curious, or anxious to know more and continue reading".
In the first few pages you have a setting involving a dark moonless night in the Caribbean that is described as being like "moist black velvet". This gives the setting an exotic location and the extreme darkness creates an uncomfortable situation. There is also the conversation of "Ship Trap Island" and how the island has a reputation so horrifying that Whitney states that "even cannibals wouldn't live in such a God-forsaken place". This gives an element of danger to the story. All of these details in setting, plus many more, help develop suspense.
You can also look at the conversations between Rainsford and Whitney and pull more details from characterization that make you want to read on.