The correct word to complete the sentence is "followed." Therefore, the full sentence would be:
"Competition was fierce. People spoke of nothing else in the days that followed, admiring the winner and promising themselves that one day, their own kite would fly proudly over the town."
We can arrive at this answer because:
Therefore, the only word capable of completing the blank space and leaving the sentence coherent and correct would be "followed."
You can find more information about what a verb is at the link:
https://brainly.com/question/854383