"The Most Dangerous Game" by Richard Connell is full of suspense, but it is most evident at the beginning of the story, when the readers do not yet know what doom is coming next.
The first example of suspense happens on the ship. Whitney is explaining the mystery surrounding Ship-Trap Island as they are passing by it in utter darkness that night. Whitney says:
"This place has an evil name among seafaring men, sir." Then he said to me, very gravely, "Don't you feel anything?"--as if the air about us was actually poisonous. Now, you mustn't laugh when I tell you this--I did feel something like a sudden chill.
Once Sanger Rainsford is alone on the deck of the ship, he is enveloped by darkness on this thickly tropical night.
An abrupt sound startled him. Off to the right he heard it, and his ears, expert in such matters, could not be mistaken. Again he heard the sound, and again. Somewhere, off in the blackness, someone had fired a gun three times.
We know that Rainsford drops his pipe and falls overboard in an attempt to catch it. What happens next is the beginning of all kinds of mysterious behavior. Rainsford is forced to swim in the blood-warm water until he reaches the rocks, and then he has to navigate those. In the middle of his efforts to arrive safely on land, this happens:
Rainsford heard a sound. It came out of the darkness, a high screaming sound, the sound of an animal in an extremity of anguish and terror.
Rainsford is an experienced hunter, and he knows the sounds of animals who are in terror. He cannot identify the sound of this one, which adds even more to the suspense of the story.
All of these examples serve to build the suspense until the narrative reaches its climax later in the story.